A165778 - OEIS

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A165778

Numbers k such that |2^k - 57| is prime.

2, 4, 6, 7, 8, 10, 16, 19, 22, 28, 43, 46, 56, 58, 62, 67, 74, 82, 140, 160, 316, 346, 376, 454, 458, 487, 580, 607, 1018, 1579, 1739, 1870, 2006, 3014, 3056, 6962, 7075, 7852, 8207, 9190, 11854, 14816, 23308, 29222, 33808, 40618, 47408, 50843, 58312, 98554

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OFFSET

1,1

COMMENTS

If p = 2^k-57 is prime, then 2^(k-1)*p is in A101260, i.e., a solution to sigma(x)-2x = 56 = 2^3*(2^3-1) = 2*A000396(2).

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

a(3) = 6 since 2^6-57 = 7 is prime.

For exponents a(1) = 2 and a(2) = 4, we get 2^a(n)-57 = -53 and -41 which are negative, but which are prime in absolute value.

MATHEMATICA

Select[Table[{n, Abs[2^n - 57]}, {n, 0, 100}], PrimeQ[#[[2]]] &][[All, 1]] (* G. C. Greubel, Apr 08 2016 *)

PROG

(PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(abs(2^n-57)), print1(n, ", "))); \\ Altug Alkan, Apr 08 2016

(Magma) [n: n in [1..1100] | IsPrime(2^n-57)]; // Vincenzo Librandi, Apr 09 2016

(Python)

from sympy import isprime, nextprime

def afind(limit):

k, pow2 = 1, 2

for k in range(1, limit+1):

if isprime(abs(pow2-57)):

print(k, end=", ")

k += 1

pow2 *= 2

afind(2100) # Michael S. Branicky, Dec 27 2021

CROSSREFS

Cf. A096818, A165779, A165780.

Sequence in context: A285140 A015932 A030493 * A286066 A139527 A163578

Adjacent sequences: A165775 A165776 A165777 * A165779 A165780 A165781

KEYWORD

nonn

AUTHOR

M. F. Hasler, Oct 11 2009

EXTENSIONS

a(36)-a(42) from Altug Alkan, Apr 08 2016

a(43)-a(44) from Michael S. Branicky, Dec 27 2021

a(45)-a(49) from Michael S. Branicky, May 14 2023

a(50) from Michael S. Branicky, Sep 25 2024

STATUS

approved