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A165779
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Numbers k such that |2^k-993| is prime.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Table[{n, Abs[2^n - 993]}, {n, 0, 100}], PrimeQ[#[[2]]] &][[All, 1]] (* G. C. Greubel, Apr 08 2016 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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