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A134694 a(0) = 2; a(n) = least prime p such that p >= a(n-1) + 2^n.

%I A134694 #10 Jan 04 2017 15:09:20
%S A134694 2,5,11,19,37,71,137,269,541,1061,2087,4139,8237,16433,32831,65599,
%T A134694 131143,262217,524369,1048661,2097257,4194409,8388733,16777381,
%U A134694 33554639,67109071,134217943,268435697,536871157,1073742073,2147483929
%N A134694 a(0) = 2; a(n) = least prime p such that p >= a(n-1) + 2^n.
%C A134694 Primes separated by at least successive powers of 2.
%H A134694 Harvey P. Dale, <a href="/A134694/b134694.txt">Table of n, a(n) for n = 0..1000</a>
%e A134694 a(0) = 2 (by definition).
%e A134694 a(1) = 5 because 5 is the least prime >= 4 = 2 + 2^1.
%e A134694 a(2) = 11 because 11 is the least prime >= 9 = 5 + 2^2.
%e A134694 a(3) = 19 because 19 is the least prime >= 19 = 11 + 2^3.
%t A134694 a = {2}; Do[i = a[[ -1]]+2^n; While[ !PrimeQ[i], i++ ]; AppendTo[a, i], {n,1,50}]; a (* _Stefan Steinerberger_, Jan 28 2008 *)
%t A134694 nxt[{n_,a_}]:={n+1,NextPrime[a+2^(n+1)-1]}; NestList[nxt,{0,2},30][[All,2]] (* _Harvey P. Dale_, Jan 04 2017 *)
%Y A134694 Cf. A000040.
%K A134694 easy,nonn
%O A134694 0,1
%A A134694 _Walter Carlini_, Jan 27 2008
%E A134694 More terms from _Stefan Steinerberger_, Jan 28 2008