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 1-3 of 3 results.

A267455 Primes which are a square (mod 39).

Original entry on oeis.org

3, 13, 43, 61, 79, 103, 127, 139, 157, 181, 199, 211, 277, 283, 313, 337, 367, 373, 433, 439, 523, 547, 571, 601, 607, 673, 727, 751, 757, 823, 829, 859, 883, 907, 919, 937, 991, 997, 1039, 1063, 1069, 1093, 1117, 1153, 1171, 1213, 1231, 1249, 1291, 1297, 1303, 1327, 1381, 1429, 1447, 1453, 1459, 1483
Offset: 1

Views

Author

M. F. Hasler, Jan 15 2016

Keywords

Comments

Motivated by the former (incorrect) definition of A191029.
Also, primes p which have Legendre symbols (p|3) = (p|13) = 1, together with 3 and 13.
Apparently this contains the 3 plus the elements of A139494. - R. J. Mathar, May 28 2025

Links

Crossrefs

Cf. A038889, A045373, A056874, A106863, A106881, A191029.
Cf. A139494.

Programs

  • Mathematica
    Join[{3, 13}, Select[Prime[Range[500]], JacobiSymbol[#, {3, 13}] == {1, 1} &]] (* Paolo Xausa, May 29 2025 *)
  • PARI
    select(p->issquare(Mod(p,39))&&isprime(p),[1..1000])

A139493 Primes of the form x^2 + 9x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

11, 23, 37, 53, 67, 71, 113, 137, 163, 179, 191, 317, 331, 379, 389, 401, 421, 443, 449, 463, 487, 499, 599, 617, 631, 641, 653, 683, 709, 751, 757, 823, 863, 883, 907, 911, 947, 977, 991, 1061, 1087, 1093, 1103, 1171, 1213, 1303, 1367, 1373, 1409, 1423
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Comments

This is a member of the family of sequences of primes of the forms x^2 + kxy + y^2.
See for k=1 A007645 = x^2+3y^2, k=2 squares no primes, k=3 A038872, k=4 A068228 = x^2+9y^2, k=5 A139492, k=6 A007519 = x^2+8y^2, k=7 A033212 = x^2+15y^2, k=8 A107152 = x^2+45y^2, k=9 A139493, k=10 A107008 = x^2+24y^2, k=11 A139494, k=12 A139495, k=13 A139496, k=14* = 10 A107008 = x^2+24y^2, k=15 A139497, k=16 A033215 = x^2+21y^2, k=17 A139498, k=18 A107145 = x^2+40y^2, k=19 A139499, k=20 A139500, k=21 A139501, k=22 A139502, k=23 A139503, k=24 A139504, k=25 A139505, k=26,A139506, k=27 A139507, k=28 A139508, k=29 A139509, k=30 A139510, k=31 A139511, k=32 A139512

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 9; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A164623 Primes p such that p*(p-1)/2-5 and p*(p-1)/2+5 are also prime numbers.

Original entry on oeis.org

13, 157, 673, 1069, 1117, 1153, 1213, 1597, 2029, 2089, 2437, 2713, 2833, 3613, 4057, 4909, 5653, 6337, 6529, 7549, 7993, 8053, 9613, 10789, 11497, 11689, 12073, 12373, 13309, 13669, 13789, 14173, 15289, 15937, 16249, 18097, 18637, 19249, 19993
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

Keywords

Comments

Primes A000040(k) such that A008837(k)+-5 are also prime numbers.

Examples

			13 is in the sequence because 13*6-5=73 and 13*6+5=83 are both prime.

Links

Crossrefs

Cf. A008846, A020882, A068228, A068229, A082539, A086519, A107159, A158708, A139494, A164620, A164621, A164622, A023203.

Programs

  • Mathematica
    Select[Prime[Range[2300]], PrimeQ[# (# - 1)/2 - 5] && PrimeQ[# (# - 1)/2 + 5] &]
  • PARI
    forprime(p=2,10^6,my(b=binomial(p,2));if(isprime(b-5)&isprime(b+5),print1(p,", "))); /* Joerg Arndt, Apr 10 2013 */

Extensions

Edited by R. J. Mathar, Aug 20 2009
Mathematica code adapted to the definition by Bruno Berselli, Apr 10 2013
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