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 1-2 of 2 results.

A247197 Primes p such that 2*p^2 + 3 and 2*p^2 + 5 are also primes.

Original entry on oeis.org

2, 7, 23, 47, 887, 1297, 1657, 2207, 2357, 2753, 4583, 4657, 6967, 8353, 8363, 10453, 12203, 12343, 13967, 16217, 16903, 21737, 23357, 23497, 25447, 29017, 32363, 36083, 40847, 41603, 41617, 43633, 45757, 46933, 48407, 52313, 60167, 60457, 66173, 67867, 71713, 72497, 72823, 73897
Offset: 1

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Author

Juri-Stepan Gerasimov, Nov 30 2014

Keywords

Comments

Primes in A247175.

Examples

			2 is in this sequence because 2*2^2 + 3 = 11, 2*2^2 + 5 = 13 and 2 are all primes.
		

Crossrefs

Programs

  • Magma
    [ n: n in [1..70000] | IsPrime(n) and IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];
  • Mathematica
    a247197[n_Integer] := Select[Prime /@ Range[n], And[PrimeQ[2*#^2 + 3], PrimeQ[2*#^2 + 5]] &]; a247197[7500] (* Michael De Vlieger, Nov 30 2014 *)
    Select[Prime[Range[7300]],AllTrue[2#^2+{3,5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 21 2019 *)

A252042 Primes p such that 2*p^3 + 1 and 2*p^3 + 3 are also primes.

Original entry on oeis.org

2, 29, 1709, 5849, 6857, 6959, 8999, 10139, 11909, 13127, 13877, 15077, 15749, 17657, 19457, 23357, 23399, 26729, 27407, 27479, 28349, 30047, 31907, 32957, 39569, 46559, 46589, 46817, 50417, 58757, 59219, 60737, 62207, 62687, 62819, 66947, 70589, 71237, 74699
Offset: 1

Views

Author

K. D. Bajpai, Dec 13 2014

Keywords

Examples

			a(2) = 29 is prime: 2*29^3 + 1 = 48779 and 2*29^3 + 3 = 48781 are both primes.
a(3) = 1709 is prime: 2*1709^3 + 1 = 9982887659 and 2*1709^3 + 3 = 9982887661 are both primes.
		

Crossrefs

Programs

  • Mathematica
    Select[Prime[Range[10000]], And[PrimeQ[2*#^3 + 1], PrimeQ[2*#^3 + 3]] &]
    Select[Prime[Range[7500]],AllTrue[2#^3+{1,3},PrimeQ]&] (* Harvey P. Dale, Apr 03 2023 *)
  • PARI
    s=[]; forprime(p=2, 10^5, if(isprime(2*p^3 + 1) && isprime(2*p^3 + 3), s=concat(s, p))); s
Showing 1-2 of 2 results.