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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A089531.

Cf. A089526, A089527, A089529.

Sequence in context: A139697 A124706 A145990 * A317986 A043190 A043970

Adjacent sequences: A089525 A089526 A089527 * A089529 A089530 A089531

Keyword

nonn

Author

Ray Chandler, Nov 07 2003

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

Status

approved