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

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%I A129919 #18 May 05 2014 14:43:27
%S A129919 5,13,19,29,37,47,131,157,139,277,179,283,127,137,577,643,181,463,919,
%T A129919 509,389,577,439,283,1511,307,317,761,787,367,389,953,971,1033,3169,
%U A129919 1093,809,1499,859,3037,541,563,577,587,1789,2309,1103,677,1601,1627
%N A129919 a(n) is the smallest prime of the form b*prime(n+1) + prime(n) with b > 0.
%C A129919 Dirichlet's theorem ensures that there always exists such a smallest prime because two primes are always coprime.
%C A129919 Corresponding values of b: 1,2,2,2,2,2,6,6,4, ... - _Zak Seidov_, Aug 29 2012
%H A129919 Harvey P. Dale, <a href="/A129919/b129919.txt">Table of n, a(n) for n = 1..1000</a>
%e A129919 a(2) is the smallest prime of the form 5*b+3 and b > 0. Hence a(2) = 13.
%t A129919 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}]
%t A129919 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 *)
%Y A129919 Cf. A035095.
%K A129919 nonn
%O A129919 1,1
%A A129919 _J. M. Bergot_, Jun 05 2007
%E A129919 Edited and extended by _Stefan Steinerberger_, Jul 16 2007