cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 15 results. Next

A112681 Primes such that the sum of the predecessor and successor primes is divisible by 3.

Original entry on oeis.org

23, 29, 31, 37, 47, 59, 61, 67, 73, 79, 83, 89, 131, 137, 151, 163, 167, 179, 199, 223, 233, 239, 251, 269, 271, 277, 331, 337, 353, 359, 367, 379, 383, 389, 433, 439, 443, 449, 467, 479, 503, 521, 523, 547, 557, 569, 571, 577, 587, 599, 601, 613, 619, 631
Offset: 1

Views

Author

Carlos Alves, Dec 30 2005

Keywords

Examples

			23 is in the sequence because 19+29=48 and 3|48.
29 is in the sequence because 29+31=60 and 3|60.

Links

Crossrefs

Analogs where 3 is replaced by other primes:
Divisor: ..3 .......5 .......7 ......11 ......13 ......17 ......19 ......23 ......29 ......31 ......37 ......41 ......43
Cf. A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@Select[Range[2, 117], Mod[Prime[ # - 1] + Prime[ # + 1], 3] == 0 &] (* Robert G. Wilson v, Jan 11 2006 *)
Select[Partition[Prime[Range[150]],3,1],Divisible[#[[1]]+#[[3]],3]&][[All,2]] (* Harvey P. Dale, Aug 18 2020 *)

A112731 Primes such that the sum of the predecessor and successor primes is divisible by 7.

Original entry on oeis.org

3, 13, 61, 71, 83, 167, 197, 241, 271, 281, 283, 317, 347, 349, 379, 431, 457, 499, 503, 569, 617, 631, 641, 643, 701, 757, 761, 797, 827, 829, 863, 1061, 1151, 1163, 1217, 1321, 1381, 1471, 1481, 1483, 1531, 1543, 1553, 1609, 1619, 1667, 1669, 1777, 1877
Offset: 1

Views

Author

Jonathan Vos Post, Dec 31 2005

Keywords

Examples

			a(1) = 3 because previousprime(3) + nextprime(3) = 2 + 5 = 7.
a(2) = 13 because previousprime(13) + nextprime(13) = 11 + 17 = 28 = 7 * 4.
a(3) = 61 because previousprime(61) + nextprime(61) = 59 + 67 = 126 = 7 * 18.
a(4) = 71 because previousprime(71) + nextprime(71) = 67 + 73 = 140 = 7 * 20.

Links

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    For[n = 2, n < 300, n++, If[(Prime[n - 1] + Prime[n + 1])/7 == Floor[(Prime[n - 1] + Prime[n + 1])/7], Print[Prime[n]]]] (* Stefan Steinerberger *)
Prime@Select[Range[2, 298], Mod[Prime[ # - 1] + Prime[ # + 1], 7] == 0 &] (* Robert G. Wilson v, Jan 11 2006 *)
Transpose[Select[Partition[Prime[Range[7000]],3,1],Divisible[First[#]+ Last[#],7]&]][[2]] (* Harvey P. Dale, Jun 11 2013 *)

Extensions

More terms from Stefan Steinerberger and Robert G. Wilson v, Jan 02 2006

A112789 Primes such that the sum of the predecessor and successor primes is divisible by 11.

Original entry on oeis.org

31, 43, 67, 109, 131, 139, 191, 617, 727, 881, 911, 937, 953, 991, 1049, 1289, 1381, 1429, 1543, 1571, 1619, 1657, 1693, 1721, 1723, 1777, 1783, 1871, 1979, 2251, 2311, 2341, 2377, 2441, 2531, 2579, 2837, 2953, 3061, 3221, 3257, 3557, 3559, 3631, 3673
Offset: 1

Views

Author

Jonathan Vos Post, Jan 01 2006

Keywords

Examples

			a(1) = 31 because prevprime(31) + nextprime(31) = 29 + 37 = 66 = 11 * 6.
a(2) = 43 because prevprime(43) + nextprime(43) = 41 + 47 = 88 = 11 * 8.
a(3) = 67 because prevprime(67) + nextprime(67) = 61 + 71 = 132 = 11 * 12.
a(4) = 109 because prevprime(109) + nextprime(109) = 107 + 113 = 220 = 11 * 20.

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@ Select[Range[2, 515], Mod[Prime[ # - 1] + Prime[ # + 1], 11] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[550]],3,1],Divisible[First[#]+ Last[#], 11]&]][[2]] (* Harvey P. Dale, Jul 22 2011 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 11. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 11.

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

A112794 Primes such that the sum of the predecessor and successor primes is divisible by 5.

Original entry on oeis.org

5, 11, 19, 41, 71, 73, 89, 97, 101, 109, 137, 149, 181, 229, 241, 281, 293, 311, 349, 359, 389, 397, 409, 419, 421, 433, 449, 457, 461, 487, 541, 557, 587, 631, 701, 709, 743, 751, 787, 811, 859, 881, 887, 919, 937, 991, 997, 1009, 1021, 1033, 1049, 1051, 1063
Offset: 1

Views

Author

Jonathan Vos Post, Jan 01 2006

Keywords

Examples

			a(1) = 5 because prevprime(5) + nextprime(5) = 3 + 7 = 10 = 5 * 2.
a(2) = 11 because prevprime(11) + nextprime(11) = 7 + 13 = 20 = 5 * 4.
a(3) = 19 because prevprime(19) + nextprime(19) = 17 + 23 = 40 = 5 * 8.
a(4) = 41 because prevprime(41) + nextprime(41) = 37 + 43 = 80 = 5 * 16.

Links

Crossrefs

Cf. A000040, A112681, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@ Select[Range[2, 179], Mod[Prime[ # - 1] + Prime[ # + 1], 5] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[200]],3,1],Divisible[#[[1]]+#[[3]],5]&] [[All,2]] (* Harvey P. Dale, May 18 2019 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 5. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 5.

Extensions

Corrected and extended by Robert G. Wilson v, Jan 05 2006

A112795 Primes such that the sum of the predecessor and successor primes is divisible by 13.

Original entry on oeis.org

79, 103, 139, 233, 271, 389, 401, 457, 587, 619, 641, 769, 883, 967, 1013, 1031, 1153, 1213, 1249, 1289, 1301, 1429, 1523, 1559, 1571, 1699, 1721, 1789, 1847, 1901, 2039, 2089, 2111, 2273, 2297, 2459, 2579, 2593, 2663, 3359, 3371, 3373, 3449, 3491, 3527
Offset: 1

Views

Author

Jonathan Vos Post, Jan 01 2006

Keywords

Comments

There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112789 is analogous to this, but mod 11.

Examples

			a(1) = 79 because prevprime(79) + nextprime(79) = 73 + 83 = 156 = 13 * 12.
a(2) = 103 because prevprime(103) + nextprime(103) = 101 + 107 = 208 = 13 * 16.
a(3) = 139 because prevprime(139) + nextprime(139) = 137 + 149 = 286 = 13 * 22.
a(4) = 233 because prevprime(233) + nextprime(233) = 229 + 239 = 468 = 13 * 36.

Links

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@ Select[Range[2, 496], Mod[Prime[ # - 1] + Prime[ # + 1], 13] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[500]],3,1],Divisible[#[[1]]+#[[3]],13]&] [[All,2]] (* Harvey P. Dale, Apr 06 2022 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 13. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 13.

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

A112796 Primes such that the sum of the predecessor and successor primes is divisible by 17.

Original entry on oeis.org

151, 191, 199, 421, 491, 613, 829, 883, 937, 1409, 1447, 1459, 1667, 1693, 1871, 2027, 2203, 2347, 2381, 2503, 2687, 2857, 2957, 3041, 3121, 3259, 3517, 3557, 3571, 3583, 3847, 3929, 4153, 4271, 4591, 4793, 4999, 5011, 5051, 5273, 5323, 5407, 5441, 5449
Offset: 1

Views

Author

Jonathan Vos Post, Jan 01 2006

Keywords

Comments

There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112789 is analogous to this, but mod 11.

Examples

			a(1) = 151 because prevprime(151) + nextprime(151) = 149 + 157 = 306 = 17 * 8.
a(2) = 191 because prevprime(191) + nextprime(191) = 181 + 193 = 374 = 17 * 22.
a(3) = 199 because prevprime(199) + nextprime(199) = 197 + 211 = 408 = 17 * 24.
a(4) = 421 because prevprime(421) + nextprime(421) = 419 + 431 = 850 = 17 * 50.

Links

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@ Select[Range[2, 731], Mod[Prime[ # - 1] + Prime[ # + 1], 17] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[800]],3,1],Divisible[#[[1]]+#[[3]],17]&][[All,2]] (* Harvey P. Dale, Oct 06 2020 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 17. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 17.

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

A112804 Primes such that the sum of the predecessor and successor primes is divisible by 19.

Original entry on oeis.org

59, 97, 683, 797, 821, 1049, 1307, 1579, 1709, 1787, 1913, 2029, 2143, 2161, 2281, 2339, 2393, 2437, 2557, 2659, 2791, 2851, 2887, 3389, 3413, 3533, 3557, 3643, 3779, 3853, 4177, 4241, 4447, 4507, 4583, 4957, 4973, 5119, 5641, 5813, 6043, 6133, 7069
Offset: 1

Views

Author

Jonathan Vos Post, Jan 01 2006

Keywords

Comments

There is a trivial analog for every prime >= 3. A112681 is analogous mod 3. A112731 is analogous mod 7. A112789 is analogous mod 11.

Examples

			a(1) = 59 because prevprime(59) + nextprime(59) = 53 + 61 = 114 = 19 * 6.
a(2) = 97 because prevprime(97) + nextprime(97) = 89 + 101 = 190 = 19 * 10.
a(3) = 683 because prevprime(683) + nextprime(683) = 677 + 691 = 1368 = 19 * 72.
a(4) = 797 because prevprime(797) + nextprime(797) = 787 + 809 = 1596 = 19 * 84.

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@ Select[Range[2, 912], Mod[Prime[ # - 1] + Prime[ # + 1], 19] == 0 &] (* Robert G. Wilson v *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 19. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 19.

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

A112847 Primes such that the sum of the predecessor and successor primes is divisible by 23.

Original entry on oeis.org

229, 277, 317, 461, 643, 919, 1033, 1307, 1427, 1609, 1777, 1789, 2089, 2207, 2347, 2531, 2551, 2647, 2969, 3121, 3169, 3517, 3659, 3701, 3727, 4211, 4421, 4549, 4903, 5039, 5309, 5431, 5867, 5881, 6091, 6211, 6277, 6673, 6781, 6803, 7309, 7499, 8147
Offset: 1

Views

Author

Jonathan Vos Post, Jan 01 2006

Keywords

Comments

There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112789 is analogous to this, but mod 11.

Examples

			a(1) = 229 because prevprime(229) + nextprime(229) = 227 + 433 = 460 = 23 * 20.
a(2) = 277 because prevprime(277) + nextprime(277) = 271 + 281 = 552 = 23 * 24.
a(3) = 317 because prevprime(317) + nextprime(317) = 313 + 331 = 644 = 23 * 28.
a(4) = 461 because prevprime(461) + nextprime(461) = 457 + 463 = 920 = 23 * 40.

Links

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@ Select[Range[2, 1032], Mod[Prime[ # - 1] + Prime[ # + 1], 23] == 0 &] (* Robert G. Wilson v, Jan 05 2006 *)
Select[Partition[Prime[Range[1100]],3,1],Divisible[#[[1]]+#[[3]],23]&][[All,2]] (* Harvey P. Dale, Jul 22 2019 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 23.
a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 23.

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

A113155 Primes such that the sum of the predecessor and successor primes is divisible by 31.

Original entry on oeis.org

311, 401, 863, 907, 1117, 1213, 1237, 1399, 1427, 2333, 3299, 3533, 3821, 3967, 4243, 4493, 5273, 5779, 6199, 6521, 7069, 8219, 8369, 8623, 8741, 8837, 8929, 9277, 9613, 10139, 10601, 10631, 10939, 11621, 11779, 12197, 12241, 12343, 12401, 12457
Offset: 1

Views

Author

Jonathan Vos Post, Jan 05 2006

Keywords

Comments

A112681 is mod 3 analogy. A112794 is mod 5 analogy. A112731 is mod 7 analogy. A112789 is mod 11 analogy. A112795 is mod 13 analogy. A112796 is mod 17 analogy. A112804 is mod 19 analogy. A112847 is mod 23 analogy. A112859 is mod 29 analogy.

Examples

			a(1) = 311 since prevprime(311) + nextprime(311) = 307 + 313 = 620 = 31 * 20.
a(2) = 401 since prevprime(401) + nextprime(401) = 397 + 409 = 806 = 31 * 26.
a(3) = 863 since prevprime(863) + nextprime(863) = 859 + 877 = 1736 = 31 * 56.
a(4) = 907 since prevprime(907) + nextprime(907) = 887 + 911 = 1798 = 31 * 58.

Links

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@Select[Range[2, 1531], Mod[Prime[ # - 1] + Prime[ # + 1], 31] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[#[[1]]+#[[3]], 31]&]][[2]] (* Harvey P. Dale, Mar 23 2012 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 31. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 31.

Extensions

Corrected and extended by Robert G. Wilson v, Jan 11 2006

A113156 Primes such that the sum of the predecessor and successor primes is divisible by 37.

Original entry on oeis.org

181, 443, 557, 661, 967, 1109, 1553, 1951, 2069, 2441, 2551, 3257, 3371, 4001, 4783, 5179, 5987, 6143, 6217, 6473, 6701, 6803, 6841, 7213, 8431, 8663, 8839, 8887, 9283, 9511, 9839, 9883, 10177, 10589, 10771, 10883, 11059, 11093, 11173, 11437, 11657
Offset: 1

Views

Author

Jonathan Vos Post, Jan 05 2006

Keywords

Comments

A112681 is mod 3 analogy. A112794 is mod 5 analogy. A112731 is mod 7 analogy. A112789 is mod 11 analogy. A112795 is mod 13 analogy. A112796 is mod 17 analogy. A112804 is mod 19 analogy. A112847 is mod 23 analogy. A112859 is mod 29 analogy.

Examples

			a(1) = 181 since prevprime(181) + nextprime(181) = 179 + 191 = 370 = 37 * 10.
a(2) = 443 since prevprime(443) + nextprime(443) = 439 + 449 = 888 = 37 * 24.
a(3) = 557 since prevprime(557) + nextprime(557) = 547 + 563 = 1110 = 37 * 30.
a(4) = 661 since prevprime(661) + nextprime(661) = 659 + 673 = 1332 = 37 * 36.

Links

Crossrefs

Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

Programs

  • Mathematica
    Prime@Select[Range[2, 1463], Mod[Prime[ # - 1] + Prime[ # + 1], 37] == 0 &] (* Robert G. Wilson v *)
Transpose[Select[Partition[Prime[Range[1500]],3,1],Divisible[First[#]+ Last[#],37]&]][[2]] (* Harvey P. Dale, Dec 19 2011 *)

Formula

a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 37. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 37.

Extensions

More terms from Robert G. Wilson v, Jan 11 2006
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