A145473 - OEIS

A145473

Primes p such that (11 + p)/2 is prime.

3, 11, 23, 47, 71, 83, 107, 131, 167, 191, 251, 263, 347, 383, 443, 467, 491, 503, 683, 827, 887, 911, 947, 971, 1031, 1103, 1163, 1187, 1223, 1283, 1307, 1427, 1511, 1583, 1607, 1667, 1811, 1847, 1871, 1931, 2027, 2087, 2111, 2207, 2351, 2423, 2447, 2543

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 11 mod 12.

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

MATHEMATICA

aa = {}; k = 11; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}]; aa

Select[Prime[Range[400]], PrimeQ[(#+11)/2]&] (* Harvey P. Dale, Apr 15 2012 *)

PROG

(PARI) first(n)=my(t=1, p, i=1); while(i<n, p=prime(i); i=i+1; if(p>2&&isprime((11+p)/2), print1(p, ", "))) \\ Anders Hellström, Jan 22 2017