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A214634 a(1) = 7; a(n) is smallest prime of the form k*a(n-1) + 3, k>0.

%I A214634 #26 Aug 02 2017 11:00:35
%S A214634 7,17,37,151,607,1217,2437,4877,39019,78041,624331,6243313,174812767,
%T A214634 1398502139,19579029949,39158059901,1957902995053,15663223960427,
%U A214634 156632239604273,3132644792085463,181693397940956857,726773591763827431,7267735917638274313,1148302274986847341457,4593209099947389365831
%N A214634 a(1) = 7; a(n) is smallest prime of the form k*a(n-1) + 3, k>0.
%H A214634 Robert Israel, <a href="/A214634/b214634.txt">Table of n, a(n) for n = 1..390</a>
%e A214634 a(2) = 17 = 2 * 7 + 3.
%e A214634 a(3) = 37 = 2 * 17 + 3.
%e A214634 a(4) = 151 = 4 * 37 + 3.
%p A214634 A214634 := proc(n)
%p A214634     option remember;
%p A214634     local k;
%p A214634     if n =  1 then
%p A214634         7;
%p A214634     else
%p A214634         for k from 1 do
%p A214634             if isprime(k*procname(n-1)+3) then
%p A214634                 return k*procname(n-1)+3 ;
%p A214634             end if;
%p A214634         end do:
%p A214634     end if;
%p A214634 end proc:
%p A214634 seq(A214634(n),n=1..20) ; # _R. J. Mathar_, Jul 23 2012
%t A214634 spf[n_]:=Module[{k=1},While[!PrimeQ[k*n+3],k++];k*n+3]; NestList[spf,7,25] (* _Harvey P. Dale_, Aug 02 2017 *)
%o A214634 (PARI)  a=7;for(n=1,200,b=a*n+3;if(isprime(b),a=b;print1(a,", ");next(n=1)))
%Y A214634 Cf. A061092, A059411, A214523, A214632, A214633
%K A214634 nonn
%O A214634 1,1
%A A214634 _Robin Garcia_, Jul 23 2012
%E A214634 More terms from _Robert Israel_, Nov 23 2016