A057776 -id:A057776 - cp's OEIS frontend

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

Labos Elemer, Nov 02 2000

nonn

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

			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.

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

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

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

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

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

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

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

A057777 a(n) is the smallest number such that a(n)+1 is a prime and the largest power of 2 which divides it is 2^n.

Original entry on oeis.org

1, 2, 4, 40, 16, 96, 192, 640, 256, 7680, 13312, 18432, 12288, 40960, 114688, 163840, 65536, 1179648, 786432, 5767168, 7340032, 23068672, 104857600, 377487360, 754974720, 167772160, 469762048, 2013265920, 3489660928, 12348030976, 3221225472, 75161927680, 184683593728

Offset: 0

Labos Elemer, Nov 02 2000

nonn

			The 4th term is 40. It is divisible by 8, 40+1 = 41 is prime. Smaller multiples of 8 are not suitable because, e.g., albeit 8|16 and 16+1 = 17 is a prime, but the largest power of 2 that divides 16 is not 8, it is 16. So 16 is not the 3rd, it is the 4th term here.

Amiram Eldar, Table of n, a(n) for n = 0..1000

Cf. A000040, A006093, A057775, A057776.

a(n) = A057775(n) - 1. - Sean A. Irvine, Jun 27 2022

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

cp's OEIS Frontend

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

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