A283957 Primes p such that 6p - 1 and 6p + 1 are twin primes and ((6p-1)^2 + (6p+1)^2) / 10 is prime.

2, 7, 17, 467, 1033, 2287, 2333, 3413, 7523, 10357, 14723, 15073, 17467, 18077, 19423, 19583, 20177, 24337, 26113, 26357, 26987, 27437, 28627, 29327, 32077, 32323, 33637, 42787, 45127, 46183, 46273, 46457, 53093, 54443, 55333, 57493, 64927, 73363, 75133, 76213, 76493, 76907, 81883, 82633, 86587

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Mar 18 2017

Keywords

• nonn

Comments

Only for prime p = 5 there are twin primes 6*5-1 = 29 and 6*5+1 = 31 such that 10 not divides (29^2 + 31^2) = 1802.

Examples

			7 is a term because 7, 6*7-1 = 41, 6*7+1 = 43, and (41^2 + 43^2)/10 = 353 are prime numbers.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A060212.

Programs

Mathematica

Select[Prime@ Range[10^4], Times @@ Boole@ Map[PrimeQ, 6 # + {-1, 1}] == 1 && PrimeQ[((6 # - 1)^2 + (6 # + 1)^2)/10] &] (* Michael De Vlieger, Mar 20 2017 *)
Select[Prime[Range[8500]],AllTrue[{6#-1,6#+1,((6#-1)^2+(6#+1)^2)/10}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 09 2018 *)

Formula

a(n) == +-2 (mod 5).