A136020 Smallest prime of the form (2*n+1)*prime(k)-2*n, any k.

7, 11, 29, 19, 23, 53, 31, 103, 191, 43, 47, 101, 109, 59, 311, 67, 71, 149, 79, 83, 173, 181, 283, 197, 103, 107, 331, 229, 709, 367, 127, 131, 269, 139, 853, 293, 151, 463, 317, 163, 167, 1021, 349, 179, 547, 373, 191, 389, 199, 607, 619, 211, 643, 1091, 223

Offset

1,1

Comments

The associated prime(k) are in A136019.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1)=7 because 7 is smallest prime p such that (p+2)/3 is prime
a(2)=11 because 11 is smallest prime p such that (p+4)/5 is prime
a(3)=29 because 29 is smallest prime p such that (p+6)/7 is prime

Mathematica

a = {}; Do[k = 1; While[ !PrimeQ[(Prime[k] + 2n)/(2n + 1)], k++ ]; AppendTo[a, Prime[k]], {n, 1, 100}]; a
Reap[Do[k = PrimePi[2n+1]; While[ !PrimeQ[((p=Prime[k]) + 2n)/(2n + 1)], k++ ]; Sow[p], {n, 100}]][[2, 1]] (* Zak Seidov, Mar 04 2013 *)

Prog

(PARI) a(n)=my(t); n+=n; forprime(p=2, default(primelimit), if(isprime(t=(n+1)*p-n), return(t))) \\ Charles R Greathouse IV, Feb 13 2011

Crossrefs

Cf. A136019, A136026, A136027.

Sequence in context: A158807 A338929 A067006 * A356467 A076304 A122560

Adjacent sequences: A136017 A136018 A136019 * A136021 A136022 A136023

Keyword

nonn,easy

Author

Artur Jasinski, Dec 10 2007

Extensions

Edited by R. J. Mathar, May 17 2009

Status

approved