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.

A164621 Primes p such that p*floor(p/2)-2 and p*floor(p/2)+2 are also prime numbers.

Original entry on oeis.org

7, 31, 79, 211, 271, 751, 787, 1231, 1447, 1459, 2347, 2551, 3727, 5119, 6427, 6691, 8467, 8707, 9007, 10099, 10531, 10567, 10831, 11959, 18691, 21487, 22039, 22567, 23059, 23167, 23371, 24379, 24499, 25171, 26371, 27967, 28579, 28591, 29287
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

Keywords

Examples

			7*3-2=13, 7*3+2=17,..

Links

Crossrefs

Cf. A068229, A158708, A164620

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p*Floor[p/2]-2]&&PrimeQ[p*Floor[p/2]+2],AppendTo[lst,p]],{n,2*7!}];lst
Select[Prime[Range[3200]],AllTrue[# Floor[#/2]+{2,-2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 04 2020 *)

A164622 Primes p such that p*floor(p/2) - 4 and p*floor(p/2) + 4 are prime numbers.

Original entry on oeis.org

151, 463, 571, 631, 643, 991, 1063, 1171, 1831, 2083, 2311, 4951, 5023, 6211, 6703, 6763, 7723, 7951, 9043, 11383, 12163, 12391, 13183, 14851, 15031, 17431, 19231, 19543, 20143, 22051, 23143, 25951, 26371, 27283, 28351, 29131, 30643, 32803
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

Keywords

Comments

151*75-4=11321 (prime), 151*75+4=11329 (prime), ..

Crossrefs

Subsequence of A068229. Cf. A008846, A020882, A068229, A086519, A158708, A164620, A164621

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p*Floor[p/2]-4]&&PrimeQ[p*Floor[p/2]+4],AppendTo[lst,p]],{n,8!}];lst

Extensions

Edited by Charles R Greathouse IV, Nov 02 2009

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
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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