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A057775 a(n) is the least prime p such that p-1 is divisible by 2^n and not by 2^(n+1).

%I A057775 #33 Mar 16 2025 13:11:38
%S A057775 2,3,5,41,17,97,193,641,257,7681,13313,18433,12289,40961,114689,
%T A057775 163841,65537,1179649,786433,5767169,7340033,23068673,104857601,
%U A057775 377487361,754974721,167772161,469762049,2013265921,3489660929,12348030977,3221225473,75161927681
%N A057775 a(n) is the least prime p such that p-1 is divisible by 2^n and not by 2^(n+1).
%C A057775 If we drop the requirement that p-1 must not be divisible by 2^(n+1), we get instead A035089, which is a nondecreasing sequence. - _Jeppe Stig Nielsen_, Aug 09 2015
%H A057775 Donovan Johnson, <a href="/A057775/b057775.txt">Table of n, a(n) for n = 0..1000</a>
%F A057775 a(n) = prime(A057776(n+1)). - _Amiram Eldar_, Mar 16 2025
%e A057775 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 A057775 f:= proc(n) local p;
%p A057775   for p from 2^n+1 by 2^(n+1) do
%p A057775     if isprime(p) then return p fi
%p A057775   od
%p A057775 end proc:
%p A057775 map(f, [$0..100]); # _Robert Israel_, Aug 10 2015
%t A057775 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 A057775 (PARI) a(n)=forstep(k=1,9e99,2,isprime((k<<n)+1)&return((k<<n)+1)) \\ _Jeppe Stig Nielsen_, Aug 09 2015
%Y A057775 Cf. A000040, A006093, A035050, A035089, A057776, A126717, A201914.
%K A057775 nonn
%O A057775 0,1
%A A057775 _Labos Elemer_, Nov 02 2000
%E A057775 More terms from Larry Reeves (larryr(AT)acm.org), Nov 03 2000