OFFSET
1,2
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).
EXAMPLE
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.
MATHEMATICA
Select[Table[{n, Abs[2^n - 993]}, {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-993)), print1(n, ", "))); \\ Altug Alkan, Apr 08 2016
(Magma) [n: n in [1..1100] |IsPrime(2^n-993)]; // 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(pow2-993)):
print(k, end=", ")
k += 1
pow2 *= 2
afind(2000) # Michael S. Branicky, Dec 26 2021
CROSSREFS
KEYWORD
nonn,more
AUTHOR
M. F. Hasler, Oct 11 2009
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
STATUS
approved