A138303 Numbers k such that k*(k+1)-1 and k*(k+1)+1 are twin primes and k*(k+3)-1 and k*(k+3)+1 are also twin primes.

3, 15, 495, 624, 1308, 1365, 1494, 1659, 1848, 6363, 8064, 12780, 13908, 14013, 16530, 18018, 18654, 28575, 30885, 31020, 38130, 43674, 48735, 50379, 57198, 60915, 61059, 62943, 75768, 76359, 76569, 80949, 81075, 83028, 84045, 86085, 88185, 104664, 105588

Offset: 1

Author

Pierre CAMI, Mar 13 2008

Keywords

• nonn

Examples

			3*4=12: 11 and 13 are twin primes; 3*6=18 and 17 and 19 are also twin primes.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 500 terms from Pierre CAMI)

Crossrefs

Subsequence of A088485.

Programs

Mathematica

Select[Range[106000],AllTrue[{#*(#+1)-1,#*(#+1)+1,#*(#+3)-1,#*(#+3)+1},PrimeQ]&] (* James C. McMahon, Jun 06 2025 *)

PARI

isok(n) = isprime(n*(n+1)-1) && isprime(n*(n+1)+1) && isprime(n*(n+3)-1) &&  isprime(n*(n+3)+1); \\ Michel Marcus, Sep 23 2019