A165779 Numbers k such that |2^k-993| is prime.

1, 4, 6, 10, 14, 17, 26, 29, 54, 62, 77, 121, 344, 476, 1012, 1717, 1954, 2929, 2993, 3014, 3304, 4704, 8882, 24042, 43572, 45722, 54913, 57893, 72566, 74473, 82092, 117302

Offset: 1

Author

M. F. Hasler, Oct 11 2009

Keywords

• nonn
• more

Comments

If p = 2^k-993 is prime, then 2^(k-1)*p is a solution to sigma(x)-2x = 992 = 2^5*(2^5-1) = 2*A000396(3).

Examples

			a(4) = 10 since 2^10-993 = 31 is prime.
For exponents a(1) = 1, a(2) = 4 and a(3) = 6, we get 2^a(n)-993 = -991, -977 and -929 which are negative, but which are prime in absolute value.
		

Crossrefs

Cf. A000396, A096818, A165778, A165780.

Programs

Magma

[n: n in [1..1100] |IsPrime(2^n-993)]; // Vincenzo Librandi, Apr 09 2016

Mathematica

Select[Table[{n, Abs[2^n - 993]}, {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-993)), print1(n, ", "))); \\ Altug Alkan, Apr 08 2016

Python

from sympy import isprime, nextprime
def afind(limit):
    k, pow2 = 1, 2
    for k in range(1, limit+1):
        if isprime(abs(pow2-993)):
            print(k, end=", ")
        k += 1
        pow2 *= 2
afind(2000) # Michael S. Branicky, Dec 26 2021

Extensions

a(23) from Altug Alkan, Apr 08 2016

a(24) from Michael S. Branicky, Dec 26 2021

a(25)-a(26) from Michael S. Branicky, Apr 06 2023

a(27)-a(32) from Michael S. Branicky, Sep 25 2024