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

2, 3, 5, 41, 17, 97, 193, 641, 257, 7681, 13313, 18433, 12289, 40961, 114689, 163841, 65537, 1179649, 786433, 5767169, 7340033, 23068673, 104857601, 377487361, 754974721, 167772161, 469762049, 2013265921, 3489660929, 12348030977, 3221225473, 75161927681

Offset: 0

Author

Labos Elemer, Nov 02 2000

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A006093, A035050, A035089, A057776, A126717, A201914.

Programs

Maple

f:= proc(n) local p;
  for p from 2^n+1 by 2^(n+1) do
    if isprime(p) then return p fi
  od
end proc:
map(f, [$0..100]); # Robert Israel, Aug 10 2015

Mathematica

Table[k = 1; While[p = k*2^n + 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}] (* T. D. Noe, Dec 27 2011 *)

PARI

a(n)=forstep(k=1,9e99,2,isprime((k<Jeppe Stig Nielsen, Aug 09 2015

Formula

a(n) = prime(A057776(n+1)). - Amiram Eldar, Mar 16 2025

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Nov 03 2000