cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

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

Views

Author

Labos Elemer, Nov 02 2000

Keywords

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.
		

Crossrefs

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

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

Views

Author

Labos Elemer, Nov 02 2000

Keywords

Examples

			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.
		

Crossrefs

Formula

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Nov 03 2000
Showing 1-2 of 2 results.