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

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

0,1

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).

Links

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

Mathematica

Table[k = 1; While[p = k*2^n - 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}]

Prog

(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

Crossrefs

Cf. A008864 (primes + 1), A057775 (p-1 case), A126717.

For n>0, sequence is first term of A002144, A007520, A141194, A142041, A142939, ...

Sequence in context: A249162 A134563 A192178 * A331217 A021398 A186631

Adjacent sequences: A201911 A201912 A201913 * A201915 A201916 A201917

Keyword

nonn

Author

T. D. Noe, Dec 27 2011

Status

approved