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

Author

Artur Jasinski, Dec 10 2007

Keywords

• nonn
• easy

Comments

The associated prime(k) are in A136019.

Examples

			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
		

Links

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

Crossrefs

Cf. A136019, A136026, A136027.

Programs

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 *)

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

Extensions

Edited by R. J. Mathar, May 17 2009