A129919 a(n) is the smallest prime of the form b*prime(n+1) + prime(n) with b > 0.

5, 13, 19, 29, 37, 47, 131, 157, 139, 277, 179, 283, 127, 137, 577, 643, 181, 463, 919, 509, 389, 577, 439, 283, 1511, 307, 317, 761, 787, 367, 389, 953, 971, 1033, 3169, 1093, 809, 1499, 859, 3037, 541, 563, 577, 587, 1789, 2309, 1103, 677, 1601, 1627

Offset: 1

Author

J. M. Bergot, Jun 05 2007

Keywords

• nonn

Comments

Dirichlet's theorem ensures that there always exists such a smallest prime because two primes are always coprime.

Corresponding values of b: 1,2,2,2,2,2,6,6,4, ... - Zak Seidov, Aug 29 2012

Examples

			a(2) is the smallest prime of the form 5*b+3 and b > 0. Hence a(2) = 13.
		

Links

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

Crossrefs

Cf. A035095.

Programs

Mathematica

a[n_] := Module[{k}, k = 1; While[Not[PrimeQ[k*Prime[n + 1] + Prime[n]]], k++ ]; k*Prime[n + 1] + Prime[n]]; Table[a[i], {i, 1, 50}]
sp[{a_,b_}]:=Module[{n=1},While[!PrimeQ[n*b+a],n++];n*b+a]; sp/@Partition[ Prime[Range[60]],2,1] (* Harvey P. Dale, Jan 02 2013 *)

Extensions

Edited and extended by Stefan Steinerberger, Jul 16 2007