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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A201914 Least prime p such that p+1 is divisible by 2^n and not by 2^(n+1).

Original entry on oeis.org

2, 5, 3, 7, 47, 31, 191, 127, 1279, 3583, 5119, 6143, 20479, 8191, 81919, 294911, 1114111, 131071, 786431, 524287, 17825791, 14680063, 138412031, 109051903, 654311423, 1912602623, 738197503, 2818572287, 7247757311, 3758096383, 228707008511, 2147483647
Offset: 0

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Author

T. D. Noe, Dec 27 2011

Keywords

Comments

See A126717 for the least k such that k*2^n-1 is prime.
For every n >= 1 there are infinitely many prime numbers p such that p + 1 is divisible by 2^n and not by 2^(n + 1). - Marius A. Burtea, Mar 10 2020

References

  • Laurențiu Panaitopol, Alexandru Gica, Arithmetic problems and number theory, Ed. Gil, Zalău, (2006), ch. 13, p. 78, pr. 5 (in Romanian).

Crossrefs

Cf. A008864 (primes + 1), A057775 (p-1 case), A126717.
For n>0, sequence is first term of A002144, A007520, A141194, A142041, A142939, ...

Programs

  • Magma
    a:=[]; for n in [0..31] do k:=1; while not IsPrime(k*2^n-1) do k:=k+2; end while; Append(~a,k*2^n-1); end for; a; // Marius A. Burtea, Mar 10 2020
  • Mathematica
    Table[k = 1; While[p = k*2^n - 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}]
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