A051645 Primes p such that 30*p+1 is also prime.

2, 5, 7, 11, 19, 23, 41, 43, 61, 67, 71, 79, 89, 109, 113, 131, 137, 167, 181, 193, 223, 229, 233, 277, 281, 313, 317, 331, 337, 359, 383, 439, 443, 457, 461, 467, 491, 503, 509, 541, 547, 593, 599, 607, 641, 691, 701, 733, 739, 743, 751, 769, 797, 821, 823

Offset

1,1

Comments

A002110(3)*p+1 and p are primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Formula

a(n) = (A051646(n)-1)/30. - Amiram Eldar, Feb 24 2025

Example

p = 19 is in the sequence because 30*p+1 = 571 is also prime.

Mathematica

Select[Prime[Range[900]], PrimeQ[30 # + 1] &] (* Vincenzo Librandi, Apr 11 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(900) | IsPrime(30*p+1)]; // Vincenzo Librandi, Apr 11 2013
(PARI) isok(k) = isprime(k) && isprime(30*k+1); \\ Amiram Eldar, Feb 24 2025

Crossrefs

Cf. A002110, A005384, A005385, A007693, A051646.

Sequence in context: A179273 A251964 A045351 * A116635 A340759 A252280

Adjacent sequences: A051642 A051643 A051644 * A051646 A051647 A051648

Keyword

nonn,easy

Author

Labos Elemer

Status

approved