%I
%S 2,3,5,41,17,97,193,641,257,7681,13313,18433,12289,40961,114689,
%T 163841,65537,1179649,786433,5767169,7340033,23068673,104857601,
%U 377487361,754974721,167772161,469762049,2013265921,3489660929,12348030977,3221225473,75161927681
%N a(n) is the least prime p such that p1 is divisible by 2^n and not by 2^(n+1).
%C If we drop the requirement that p1 must not be divisible by 2^(n+1), we get instead A035089, which is a nondecreasing sequence.  _Jeppe Stig Nielsen_, Aug 09 2015
%H Donovan Johnson, <a href="/A057775/b057775.txt">Table of n, a(n) for n = 0..1000</a>
%e a(13) = 40961 = 1 + 8192*5 where the last term is divisible by the 13th power of 2 and 40961 is the smallest prime with that property.
%p f:= proc(n) local p;
%p for p from 2^n+1 by 2^(n+1) do
%p if isprime(p) then return p fi
%p od
%p end proc:
%p map(f, [$0..100]); # _Robert Israel_, Aug 10 2015
%t Table[k = 1; While[p = k*2^n + 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}] (* _T. D. Noe_, Dec 27 2011 *)
%o (PARI) a(n)=forstep(k=1,9e99,2,isprime((k<<n)+1)&return((k<<n)+1)) \\ _Jeppe Stig Nielsen_, Aug 09 2015
%Y Cf. A000040, A006093, A035050, A035089, A126717, A201914.
%K nonn
%O 0,1
%A _Labos Elemer_, Nov 02 2000
%E More terms from Larry Reeves (larryr(AT)acm.org), Nov 03 2000
