A089528 Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.

13, 37, 89, 277, 389, 397, 449, 457, 701, 761, 929, 2069, 2221, 2609, 2857, 3121, 3217, 3221, 6329, 7229, 7537, 7649, 8581, 8677, 9277, 9941, 11317, 11681, 12401, 13421, 13469, 15649, 16729, 17401, 17497, 17729, 18257, 19289, 19489, 19937, 20509

Offset: 1

Author

Ray Chandler, Nov 07 2003

Keywords

• nonn

Examples

			p(3)=5, 2*5 + 3 = 13 = p(6);
p(4)=7, 2*7 + 3 = 17 = p(7).
		

Links

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

Crossrefs

Subsequence of A089531.

Cf. A089526, A089527, A089529.

Programs

Mathematica

Select[Partition[2#+3&/@Prime[Range[2500]],2,1],AllTrue[#,PrimeQ] && NextPrime[ #[[1]]]==#[[2]]&][[All,1]] (* Harvey P. Dale, Dec 14 2021 *)

PARI

forprime(p=2,10500,my(p23=2*p+3);if(isprime(p23),my(pp=2*nextprime(p+1)+3);if(isprime(pp)&&pp==nextprime(p23+1),print1(p23,", ")))) \\ Hugo Pfoertner, Aug 04 2021

Formula

a(n) = 2*A089527(n) + 3 = 2*A000040(A089526(n)) + 3 = A000040(A089529(n)).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 04 2021