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
Offset: 1
Keywords
Examples
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.
Programs
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Magma
[n: n in [1..1100] | IsPrime(2^n-57)]; // Vincenzo Librandi, Apr 09 2016
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Mathematica
Select[Table[{n, Abs[2^n - 57]}, {n, 0, 100}], PrimeQ[#[[2]]] &][[All,1]] (* G. C. Greubel, Apr 08 2016 *) -
PARI
lista(nn) = for(n=1, nn, if(ispseudoprime(abs(2^n-57)), print1(n, ", "))); \\ Altug Alkan, Apr 08 2016
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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
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
Comments