A191473 - OEIS

A191473

Let a(1) = 3. For n > 1, a(n) is the smallest prime p > a(n-1) such that q = (a(n-1) + p)/4 is prime.

%I #9 Nov 25 2013 13:57:37

%S 3,5,7,13,31,37,79,109,127,157,199,229,367,397,607,661,727,829,967,

%T 997,1039,1213,1399,1693,1759,1789,1999,2053,2143,2221,2383,2389,2503,

%U 3229,3319,3469,3823,4093,4159,4357,4591,4597,4639,4789,4903,4933,5431,5581

%N Let a(1) = 3. For n > 1, a(n) is the smallest prime p > a(n-1) such that q = (a(n-1) + p)/4 is prime.

%C Corresponding values of q: 2, 3, 5, 11, 17, 29, 47, 59, 71, 89, 107.

%H Zak Seidov, <a href="/A191473/b191473.txt">Table of n, a(n) for n = 1..1000</a>

%t p=3; s={p}; Do[q=Prime[n]; If[PrimeQ[(p+q)/4], AppendTo[s,q]; p=q], {n, 3, 1000}]; s

%t nxt[n_]:=Module[{p=NextPrime[n]},While[!PrimeQ[(n+p)/4],p=NextPrime[ p]]; p]; NestList[nxt,3,50] (* _Harvey P. Dale_, Nov 25 2013 *)

%Y Cf. A126938.

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 27 2012