A057160 Smallest value of k for which the expression k*2^(2^n-1)-1 is prime.

3, 2, 1, 1, 4, 1, 6, 1, 90, 111, 244, 139, 880, 309, 22263, 56083, 130141, 49905

Offset

0,1

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = A053989(A058891(n+1)). - Pontus von Brömssen, May 27 2022

Example

a(1)=2 because 2*2^(2^1-1)-1 = 2*2^1-1 = 3 which is prime. - Sean A. Irvine, May 25 2022
a(4)=4 because 4*2^(2^4-1)-1 = 4*2^15-1 = 4*32768-1 = 131071 which is prime.

Mathematica

svk[n_]:= Module[{k = 1, c = 2^(2^n-1)}, While[!PrimeQ[k*c-1], k++]; k]; Join[{2}, svk /@ Range[17]] (* Harvey P. Dale, Feb 03 2021, adjusted for new offset by Michael De Vlieger, May 25 2022 *)

Prog

(Python)
from sympy import isprime
def a(n):
    k, c = 1, 2**(2**n-1)
    while not isprime(k*c - 1): k += 1
    return k
print([a(n) for n in range(1, 12)]) # Michael S. Branicky, May 25 2022
(PARI) a(n) = my(k=1); while (!isprime(k*2^(2^n-1)-1), k++); k; \\ Michel Marcus, May 27 2022

Crossrefs

Cf. A053989, A058891, A077585 (2^(2^n-1)-1).

Sequence in context: A373377 A053989 A342459 * A239938 A097794 A275494

Adjacent sequences: A057157 A057158 A057159 * A057161 A057162 A057163

Keyword

nonn,more

Author

Steven Harvey, Sep 14 2000

Extensions

Offset and a(1) corrected by Sean A. Irvine, May 25 2022

a(0) prepended by Michel Marcus, May 27 2022

Status

approved