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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). 10

%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 p-1 is divisible by 2^n and not by 2^(n+1).

%C 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 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

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Last modified October 14 14:45 EDT 2019. Contains 328019 sequences. (Running on oeis4.)