Inhaltsverzeichnis

Development of
Algorithmic Constructions

03:35:51
Deutsch
29.Mar 2024

Polynom = x^2-24x+3607

0. Sequence

1. Algorithm

2. Mathematical background

3. Correctness of the algorithm

4. Infinity of the sequence

5. Sequence of the polynom with 1

6. Sequence of the polynom (only primes)

7. Distribution of the primes

8. Check for existing Integer Sequences by OEIS

0. Sequence

f(0) = 3607 = 3607
f(1) = 7 = 7
f(2) = 3563 = 7*509
f(3) = 443 = 443
f(4) = 3527 = 3527
f(5) = 439 = 439
f(6) = 3499 = 3499
f(7) = 109 = 109
f(8) = 3479 = 7*7*71
f(9) = 217 = 7*31
f(10) = 3467 = 3467
f(11) = 433 = 433
f(12) = 3463 = 3463
f(13) = 433 = 433
f(14) = 3467 = 3467
f(15) = 217 = 7*31
f(16) = 3479 = 7*7*71
f(17) = 109 = 109
f(18) = 3499 = 3499
f(19) = 439 = 439
f(20) = 3527 = 3527
f(21) = 443 = 443
f(22) = 3563 = 7*509
f(23) = 7 = 7
f(24) = 3607 = 3607
f(25) = 227 = 227
f(26) = 3659 = 3659
f(27) = 461 = 461
f(28) = 3719 = 3719
f(29) = 469 = 7*67
f(30) = 3787 = 7*541
f(31) = 239 = 239
f(32) = 3863 = 3863
f(33) = 61 = 61
f(34) = 3947 = 3947
f(35) = 499 = 499
f(36) = 4039 = 7*577
f(37) = 511 = 7*73
f(38) = 4139 = 4139
f(39) = 131 = 131
f(40) = 4247 = 31*137
f(41) = 269 = 269
f(42) = 4363 = 4363
f(43) = 553 = 7*79
f(44) = 4487 = 7*641
f(45) = 569 = 569
f(46) = 4619 = 31*149
f(47) = 293 = 293
f(48) = 4759 = 4759
f(49) = 151 = 151
f(50) = 4907 = 7*701
f(51) = 623 = 7*89
f(52) = 5063 = 61*83
f(53) = 643 = 643
f(54) = 5227 = 5227
f(55) = 83 = 83
f(56) = 5399 = 5399
f(57) = 343 = 7*7*7
f(58) = 5579 = 7*797
f(59) = 709 = 709
f(60) = 5767 = 73*79
f(61) = 733 = 733
f(62) = 5963 = 67*89
f(63) = 379 = 379
f(64) = 6167 = 7*881
f(65) = 49 = 7*7
f(66) = 6379 = 6379
f(67) = 811 = 811
f(68) = 6599 = 6599
f(69) = 839 = 839
f(70) = 6827 = 6827
f(71) = 217 = 7*31
f(72) = 7063 = 7*1009
f(73) = 449 = 449
f(74) = 7307 = 7307
f(75) = 929 = 929
f(76) = 7559 = 7559
f(77) = 961 = 31*31
f(78) = 7819 = 7*1117
f(79) = 497 = 7*71
f(80) = 8087 = 8087
f(81) = 257 = 257
f(82) = 8363 = 8363
f(83) = 1063 = 1063
f(84) = 8647 = 8647
f(85) = 1099 = 7*157
f(86) = 8939 = 7*1277
f(87) = 71 = 71
f(88) = 9239 = 9239
f(89) = 587 = 587
f(90) = 9547 = 9547
f(91) = 1213 = 1213
f(92) = 9863 = 7*1409
f(93) = 1253 = 7*179
f(94) = 10187 = 61*167
f(95) = 647 = 647
f(96) = 10519 = 67*157
f(97) = 167 = 167
f(98) = 10859 = 10859
f(99) = 1379 = 7*197
f(100) = 11207 = 7*1601

1. Algorithm

If you are interested in some better algorithms have a look at quadr_Sieb_x^2+1.php.

2. Mathematical background

Lemma: If p | f(x) then also p | f(x+p) and p | f(-x-b/a) a) p | f(x) <=> ax^2 + bx + c = 0 mod p p | f(x+p) <=> a(x+p)^2 + b(x+p) + c = 0 mod p <=> ax^2 + 2axp + ap^2 + bx + bp + c = 0 mod p <=> ax^2 + bx + c = 0 mod p Thus if p | f(x) then p | f(x+p) b) if b = 0 mod a p | f(x) <=> ax^2 + bx + c = 0 mod p p | f(-x-b/a) <=> a(-x-b/a)^2 + b(-x-b/a) + c = 0 mod p <=> ax^2 + 2bx + b^2/a - bx - b^2/a + c = 0 mod p <=> ax^2 + bx + c = 0 mod p Thus if p | f(x) then p | f(-x-b/a)

3. Correctness of the algorithm

The proof for this polynom is similar to the proof for the polynom f(x)=x^2-4x+1. a) First terms for the polynom f(x) = x^2-24x+3607

f(0)=3607
f(1)=7
f(2)=509
f(3)=443
f(4)=3527
f(5)=439
f(6)=3499
f(7)=109
f(8)=71
f(9)=31
f(10)=3467
f(11)=433
f(12)=3463
f(13)=1
f(14)=1
f(15)=1
f(16)=1
f(17)=1
f(18)=1
f(19)=1
f(20)=1
f(21)=1
f(22)=1
f(23)=1
f(24)=1
f(25)=227
f(26)=3659
f(27)=461
f(28)=3719
f(29)=67
f(30)=541
f(31)=239
f(32)=3863
f(33)=61
f(34)=3947
f(35)=499
f(36)=577
f(37)=73
f(38)=4139
f(39)=131
f(40)=137
f(41)=269
f(42)=4363
f(43)=79
f(44)=641
f(45)=569
f(46)=149
f(47)=293
f(48)=4759
f(49)=151
f(50)=701
f(51)=89
f(52)=83
f(53)=643
f(54)=5227
f(55)=1
f(56)=5399
f(57)=1
f(58)=797
f(59)=709
f(60)=1
f(61)=733
f(62)=1
f(63)=379
f(64)=881
f(65)=1
f(66)=6379
f(67)=811
f(68)=6599
f(69)=839
f(70)=6827
f(71)=1
f(72)=1009
f(73)=449
f(74)=7307
f(75)=929
f(76)=7559
f(77)=1
f(78)=1117
f(79)=1
f(80)=8087
f(81)=257
f(82)=8363
f(83)=1063
f(84)=8647
f(85)=157
f(86)=1277
f(87)=1
f(88)=9239
f(89)=587
f(90)=9547
f(91)=1213
f(92)=1409
f(93)=179
f(94)=167
f(95)=647
f(96)=1
f(97)=1
f(98)=10859
f(99)=197

b) Substitution of the polynom
The polynom f(x)=x^2-24x+3607 could be written as f(y)= y^2+3463 with x=y+12

c) Backsubstitution Beside by backsubstitution you get an estimation for the huge of the primes with p | f(x) and p < f(x) f'(y)>(2y-1) with with y=x-12
f'(x)>2x-25 with x > 59

4. Infinity of the sequence

The mathematical proof is analogue to the proof for the polynom f(x)=x^2+1

5. Sequence of the polynom with 1

3607, 7, 509, 443, 3527, 439, 3499, 109, 71, 31, 3467, 433, 3463, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 227, 3659, 461, 3719, 67, 541, 239, 3863, 61, 3947, 499, 577, 73, 4139, 131, 137, 269, 4363, 79, 641, 569, 149, 293, 4759, 151, 701, 89, 83, 643, 5227, 1, 5399, 1, 797, 709, 1, 733, 1, 379, 881, 1, 6379, 811, 6599, 839, 6827, 1, 1009, 449, 7307, 929, 7559, 1, 1117, 1, 8087, 257, 8363, 1063, 8647, 157, 1277, 1, 9239, 587, 9547, 1213, 1409, 179, 167, 647, 1, 1, 10859, 197, 1601, 1423, 373, 367, 11927, 757, 251, 223, 409, 1609, 1, 829, 13463, 1, 283, 1759, 1, 1811, 14699, 233, 2161, 1, 1, 1973, 16007, 2029, 1, 1, 2417, 1, 17387, 2203, 17863, 1, 2621, 1, 18839, 1193, 1, 1, 1, 359, 2909, 1289, 20887, 661, 21419, 2711, 3137, 397, 317, 1, 23063, 1459, 23627, 1, 3457, 3061, 349, 1567, 25367, 401, 3709, 1, 857, 3359, 27179, 859, 27799, 1, 1, 3593, 29063, 3673, 487, 1877, 4337, 1, 31019, 3919, 31687, 4003, 32363, 1, 4721, 2087, 33739, 4261, 34439, 4349, 5021, 1, 35863, 1, 36587, 1, 557, 673, 5437, 1201, 1, 1, 39563, 4993, 823, 727, 563, 2593, 41879, 1321, 42667, 769, 887, 5483, 44267, 1, 739, 2843, 1, 827, 46727, 1, 47563, 2999, 48407, 1, 1, 6211, 50119, 1, 761, 1607, 1, 467, 52747, 1, 53639, 6761, 54539, 491, 1, 1747, 1, 7103, 57287, 7219, 8317, 1, 59159, 3727, 60107, 7573, 1, 1, 8861, 3907, 863, 1, 1, 8059, 9281, 1, 65963, 1, 1, 4217, 67979, 1223, 9857, 8689, 1, 4409, 1, 2237, 10301, 1297, 1, 1, 74219, 1, 953, 677, 10909, 9613, 77447, 9749, 78539, 4943, 1, 1, 80747, 10163, 1153, 10303, 2677, 1, 1, 1, 85259, 10729, 1217, 1, 1787, 787, 1069, 2791, 89899, 11311, 91079, 1637, 1, 1451, 93463, 5879, 691, 11909, 13697, 1723, 1091, 1, 98327, 773, 99563, 1789, 14401, 1, 102059, 3209, 103319, 1, 1, 1879, 105863, 13313, 983, 6737, 108439, 1, 1, 13799, 1, 13963, 112363, 883, 1, 1021, 115019, 14461, 116359, 14629, 3797, 1, 1, 1871, 120427, 15139, 3929, 1, 17597, 1, 124567, 7829, 125963, 1, 1901, 2287, 18397, 8093, 130199, 4091, 131627, 1, 19009, 2389, 134507, 2113, 1721, 8543, 1049, 2467, 19841, 1, 140363, 8819, 1709, 1, 20477, 1, 144839, 18199, 146347, 4597, 147863, 1327, 21341, 1, 150919, 1, 152459, 1, 1, 1, 2131, 19543, 157127, 19739, 158699, 1, 3271, 10067, 1031, 20333, 5273, 20533, 23581, 1481, 166679, 2617, 1, 21139, 1, 3049, 24509, 5387, 173207, 1, 174859, 21961, 1, 3167, 178187, 1, 1373, 5647, 2557, 3257, 26177, 23011, 2341, 2903, 186647, 11719, 1, 1, 1, 23869, 1, 12043, 193559, 1, 27901, 1, 197063, 1, 198827, 1, 28657, 1, 1, 25409, 3347, 25633, 205963, 1847, 1, 6521, 209579, 1, 1181, 26539, 1, 1, 215063, 13499, 6997, 1, 1, 3923, 31517, 1, 7177, 3491, 224363, 28163, 32321, 4057, 228139, 7159, 1, 14437, 231947, 4159, 33409, 1, 235787, 14797, 2671, 7459, 1, 4297, 1, 30323, 1613, 3821, 245527, 1, 5051, 1, 1, 1, 251467, 1, 36209, 1, 255467, 32059, 1307, 1, 259499, 1163, 37361, 1, 1, 33073, 265607, 33329, 38237, 2399, 269719, 8461, 271787, 1, 1999, 4909, 1, 1, 8969, 17443, 280139, 35149, 1, 5059, 9173, 17839, 286487, 4493, 1, 1, 1, 36479, 3529, 9187, 2707, 1, 42461, 1, 1907, 37561, 301579, 18917, 303767, 1361, 1, 1, 1, 1, 310379, 1, 44657, 2801, 314827, 1, 317063, 1283, 2143, 2861, 1, 2521, 323819, 1, 326087, 40903, 1, 1471, 4657, 1, 1493, 41761, 2447, 6007, 48221, 21169, 339863, 10657, 342187, 1, 1, 6173, 1, 2719, 349207, 1, 351563, 6299, 1, 44389, 356299, 22343, 1429, 5623, 51581, 6469, 363463, 1, 1, 11471, 368279, 3299, 52957, 46489, 373127, 1, 375563, 23549, 54001, 1693, 380459, 47711, 382919, 1549, 2153, 1, 1, 1, 390347, 1579, 4733, 49261, 56477, 3541, 3037, 1559, 2687, 1, 5519, 1, 57917, 1, 407959, 25577, 410507, 51473, 59009, 1, 415627, 1, 418199, 13109, 420779, 7537, 1951, 1, 6983, 1669, 428567, 1, 1987, 7723, 1, 1, 436427, 1, 439063, 1, 1, 1, 1, 55711, 447019, 14011, 1, 4027, 452363, 56713, 455047, 1, 457739, 4099, 65777, 14431, 2351, 1873, 5897, 58403, 1, 1, 1, 1, 474059, 1, 1, 8539, 9787, 30059, 7907, 3779, 2137, 60811, 69697, 8737, 2053, 15377, 493463, 1, 1931, 8887, 1, 1, 7069, 1, 504727, 15817, 2339, 1, 3251, 1, 7229, 4021, 16649, 4621, 1, 65053, 7789, 65413, 1, 32887, 75377, 1, 530539, 66499, 533447, 66863, 1, 1, 77041, 33797, 542219, 67961, 2281, 68329, 78301, 1, 551063, 1, 7013, 69439, 556999, 9973, 79997, 1, 562967, 35279, 3389, 1, 81281, 1, 8537, 1, 1, 1, 5303, 1, 83009, 72823, 6563, 18301, 2633, 36793, 84317, 10567, 5443, 74353, 596363, 37369, 1, 2683, 86077, 75511, 605639, 1, 1, 1, 12487, 5477, 1, 77069, 618119, 1, 621259, 1, 12743, 9781, 7561, 78643, 4177, 79039, 1, 2837, 637079, 1, 640267, 80233, 643463, 11519, 92381, 1, 649879, 20359, 2803, 81839, 93761, 1, 659563, 10331, 1, 1, 1, 11923, 95617, 83869, 672587, 42139, 675863, 1, 97021, 12157, 682439, 1, 685739, 21481, 9439, 1, 98909, 86753, 695687, 1, 22549, 43793, 1, 1, 8933, 88423, 1, 88843, 712427, 1, 1, 44843, 719179, 1, 10177, 90533, 1, 1, 729367, 11423, 10937, 91811, 10369, 13177, 1, 23167, 4987, 46549, 746507, 93529, 107137, 1, 1, 1, 756887, 1, 9161, 1, 109121, 1, 767339, 1, 770839, 1, 15803, 13859, 777863, 97453, 781387, 48947, 784919, 1, 16091, 98779, 11821, 99223, 6073, 24917, 114161, 7151, 13159, 1, 1, 101009, 4111, 7247, 1, 1, 26357, 102359, 820679, 102811, 117757, 1, 827927, 51859, 3313, 104173, 835207, 14947, 1, 52543, 842519, 1, 846187, 1, 1, 1, 853547, 26731, 11743, 53693, 860939, 1, 1, 1, 1, 1, 1, 1, 125117, 2239, 14419, 1, 883307, 13831, 9967, 7937, 127261, 1, 6829, 112061, 1, 56267, 1, 1, 905963, 1, 909767, 1, 913579, 1, 1, 57457, 29717, 1, 925063, 115873, 132701, 8311, 30089, 29209, 936619, 117319, 1, 16829, 134909, 7393, 948247, 59387, 13043, 1, 1, 17107, 959947, 1, 963863, 15091, 967787, 17317, 2833, 121711, 8951, 1,

6. Sequence of the polynom (only primes)

3607, 7, 509, 443, 3527, 439, 3499, 109, 71, 31, 3467, 433, 3463, 227, 3659, 461, 3719, 67, 541, 239, 3863, 61, 3947, 499, 577, 73, 4139, 131, 137, 269, 4363, 79, 641, 569, 149, 293, 4759, 151, 701, 89, 83, 643, 5227, 5399, 797, 709, 733, 379, 881, 6379, 811, 6599, 839, 6827, 1009, 449, 7307, 929, 7559, 1117, 8087, 257, 8363, 1063, 8647, 157, 1277, 9239, 587, 9547, 1213, 1409, 179, 167, 647, 10859, 197, 1601, 1423, 373, 367, 11927, 757, 251, 223, 409, 1609, 829, 13463, 283, 1759, 1811, 14699, 233, 2161, 1973, 16007, 2029, 2417, 17387, 2203, 17863, 2621, 18839, 1193, 359, 2909, 1289, 20887, 661, 21419, 2711, 3137, 397, 317, 23063, 1459, 23627, 3457, 3061, 349, 1567, 25367, 401, 3709, 857, 3359, 27179, 859, 27799, 3593, 29063, 3673, 487, 1877, 4337, 31019, 3919, 31687, 4003, 32363, 4721, 2087, 33739, 4261, 34439, 4349, 5021, 35863, 36587, 557, 673, 5437, 1201, 39563, 4993, 823, 727, 563, 2593, 41879, 1321, 42667, 769, 887, 5483, 44267, 739, 2843, 827, 46727, 47563, 2999, 48407, 6211, 50119, 761, 1607, 467, 52747, 53639, 6761, 54539, 491, 1747, 7103, 57287, 7219, 8317, 59159, 3727, 60107, 7573, 8861, 3907, 863, 8059, 9281, 65963, 4217, 67979, 1223, 9857, 8689, 4409, 2237, 10301, 1297, 74219, 953, 677, 10909, 9613, 77447, 9749, 78539, 4943, 80747, 10163, 1153, 10303, 2677, 85259, 10729, 1217, 1787, 787, 1069, 2791, 89899, 11311, 91079, 1637, 1451, 93463, 5879, 691, 11909, 13697, 1723, 1091, 98327, 773, 99563, 1789, 14401, 102059, 3209, 103319, 1879, 105863, 13313, 983, 6737, 108439, 13799, 13963, 112363, 883, 1021, 115019, 14461, 116359, 14629, 3797, 1871, 120427, 15139, 3929, 17597, 124567, 7829, 125963, 1901, 2287, 18397, 8093, 130199, 4091, 131627, 19009, 2389, 134507, 2113, 1721, 8543, 1049, 2467, 19841, 140363, 8819, 1709, 20477, 144839, 18199, 146347, 4597, 147863, 1327, 21341, 150919, 152459, 2131, 19543, 157127, 19739, 158699, 3271, 10067, 1031, 20333, 5273, 20533, 23581, 1481, 166679, 2617, 21139, 3049, 24509, 5387, 173207, 174859, 21961, 3167, 178187, 1373, 5647, 2557, 3257, 26177, 23011, 2341, 2903, 186647, 11719, 23869, 12043, 193559, 27901, 197063, 198827, 28657, 25409, 3347, 25633, 205963, 1847, 6521, 209579, 1181, 26539, 215063, 13499, 6997, 3923, 31517, 7177, 3491, 224363, 28163, 32321, 4057, 228139, 7159, 14437, 231947, 4159, 33409, 235787, 14797, 2671, 7459, 4297, 30323, 1613, 3821, 245527, 5051, 251467, 36209, 255467, 32059, 1307, 259499, 1163, 37361, 33073, 265607, 33329, 38237, 2399, 269719, 8461, 271787, 1999, 4909, 8969, 17443, 280139, 35149, 5059, 9173, 17839, 286487, 4493, 36479, 3529, 9187, 2707, 42461, 1907, 37561, 301579, 18917, 303767, 1361, 310379, 44657, 2801, 314827, 317063, 1283, 2143, 2861, 2521, 323819, 326087, 40903, 1471, 4657, 1493, 41761, 2447, 6007, 48221, 21169, 339863, 10657, 342187, 6173, 2719, 349207, 351563, 6299, 44389, 356299, 22343, 1429, 5623, 51581, 6469, 363463, 11471, 368279, 3299, 52957, 46489, 373127, 375563, 23549, 54001, 1693, 380459, 47711, 382919, 1549, 2153, 390347, 1579, 4733, 49261, 56477, 3541, 3037, 1559, 2687, 5519, 57917, 407959, 25577, 410507, 51473, 59009, 415627, 418199, 13109, 420779, 7537, 1951, 6983, 1669, 428567, 1987, 7723, 436427, 439063, 55711, 447019, 14011, 4027, 452363, 56713, 455047, 457739, 4099, 65777, 14431, 2351, 1873, 5897, 58403, 474059, 8539, 9787, 30059, 7907, 3779, 2137, 60811, 69697, 8737, 2053, 15377, 493463, 1931, 8887, 7069, 504727, 15817, 2339, 3251, 7229, 4021, 16649, 4621, 65053, 7789, 65413, 32887, 75377, 530539, 66499, 533447, 66863, 77041, 33797, 542219, 67961, 2281, 68329, 78301, 551063, 7013, 69439, 556999, 9973, 79997, 562967, 35279, 3389, 81281, 8537, 5303, 83009, 72823, 6563, 18301, 2633, 36793, 84317, 10567, 5443, 74353, 596363, 37369, 2683, 86077, 75511, 605639, 12487, 5477, 77069, 618119, 621259, 12743, 9781, 7561, 78643, 4177, 79039, 2837, 637079, 640267, 80233, 643463, 11519, 92381, 649879, 20359, 2803, 81839, 93761, 659563, 10331, 11923, 95617, 83869, 672587, 42139, 675863, 97021, 12157, 682439, 685739, 21481, 9439, 98909, 86753, 695687, 22549, 43793, 8933, 88423, 88843, 712427, 44843, 719179, 10177, 90533, 729367, 11423, 10937, 91811, 10369, 13177, 23167, 4987, 46549, 746507, 93529, 107137, 756887, 9161, 109121, 767339, 770839, 15803, 13859, 777863, 97453, 781387, 48947, 784919, 16091, 98779, 11821, 99223, 6073, 24917, 114161, 7151, 13159, 101009, 4111, 7247, 26357, 102359, 820679, 102811, 117757, 827927, 51859, 3313, 104173, 835207, 14947, 52543, 842519, 846187, 853547, 26731, 11743, 53693, 860939, 125117, 2239, 14419, 883307, 13831, 9967, 7937, 127261, 6829, 112061, 56267, 905963, 909767, 913579, 57457, 29717, 925063, 115873, 132701, 8311, 30089, 29209, 936619, 117319, 16829, 134909, 7393, 948247, 59387, 13043, 17107, 959947, 963863, 15091, 967787, 17317, 2833, 121711, 8951,

7. Distribution of the primes

Legend of the table: I distinguish between primes p= x^2-24x+3607 and
the reducible primes which appear as divisor for the first time
p | x^2-24x+3607 and p < x^2-24x+3607

To avoid confusion with the number of primes:
I did not count the primes <= A
but I counted the primes appending the x and therefore the x <= A

A B C D E F G H
exponent
=log2 (x)
<=x number
of all primes
number of primes
p = f(x)
number of primes
p | f(x)
C / x D / x E / x
1 2 3 1 2 1.5 0.5 1
2 4 5 2 3 1.25 0.5 0.75
3 8 9 3 6 1.125 0.375 0.75
4 16 13 5 8 0.8125 0.3125 0.5
5 32 21 8 13 0.65625 0.25 0.40625
6 64 49 14 35 0.765625 0.21875 0.546875
7 128 99 29 70 0.7734375 0.2265625 0.546875
8 256 196 61 135 0.765625 0.23828125 0.52734375
9 512 381 111 270 0.74414063 0.21679688 0.52734375
10 1024 743 203 540 0.72558594 0.19824219 0.52734375
11 2048 1473 367 1106 0.71923828 0.17919922 0.54003906
12 4096 2931 652 2279 0.71557617 0.15917969 0.55639648
13 8192 5838 1192 4646 0.71264648 0.14550781 0.56713867
14 16384 11616 2198 9418 0.70898438 0.13415527 0.5748291
15 32768 23171 4093 19078 0.7071228 0.12490845 0.58221436
16 65536 46276 7591 38685 0.70611572 0.11582947 0.59028625
17 131072 92383 14205 78178 0.70482635 0.10837555 0.59645081
18 262144 184565 26506 158059 0.7040596 0.10111237 0.60294724
19 524288 368668 49925 318743 0.70317841 0.09522438 0.60795403
20 1048576 736700 94469 642231 0.70257187 0.09009266 0.61247921
21 2097152 1472182 179362 1292820 0.70199108 0.08552647 0.61646461
22 4194304 2942000 341031 2600969 0.70142746 0.08130813 0.62011933
23 8388608 5880300 650401 5229899 0.70098639 0.07753384 0.62345254
24 16777216 11754418 1242153 10512265 0.70061791 0.07403809 0.62657982


8. Check for existing Integer Sequences by OEIS

Found in Database : 3607, 7, 509, 443, 3527, 439, 3499, 109, 71, 31, 3467, 433, 3463, 1, 1, 1, 1, 1, 1, 1,
Found in Database : 3607, 7, 509, 443, 3527, 439, 3499, 109, 71, 31, 3467, 433, 3463, 227, 3659, 461, 3719, 67, 541, 239, 3863, 61, 3947, 499, 577, 73, 4139, 131,
Found in Database : 7, 31, 61, 67, 71, 73, 79, 83, 89, 109, 131, 137, 149,