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A057160
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Smallest value of k for which the expression k*2^(2^n-1)-1 is prime.
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0
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3, 2, 1, 1, 4, 1, 6, 1, 90, 111, 244, 139, 880, 309, 22263, 56083, 130141, 49905
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OFFSET
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0,1
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LINKS
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FORMULA
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EXAMPLE
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a(1)=2 because 2*2^(2^1-1)-1 = 2*2^1-1 = 3 which is prime. - Sean A. Irvine, May 25 2022
a(4)=4 because 4*2^(2^4-1)-1 = 4*2^15-1 = 4*32768-1 = 131071 which is prime.
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MATHEMATICA
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svk[n_]:= Module[{k = 1, c = 2^(2^n-1)}, While[!PrimeQ[k*c-1], k++]; k]; Join[{2}, svk /@ Range[17]] (* Harvey P. Dale, Feb 03 2021, adjusted for new offset by Michael De Vlieger, May 25 2022 *)
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PROG
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(Python)
from sympy import isprime
def a(n):
k, c = 1, 2**(2**n-1)
while not isprime(k*c - 1): k += 1
return k
(PARI) a(n) = my(k=1); while (!isprime(k*2^(2^n-1)-1), k++); k; \\ Michel Marcus, May 27 2022
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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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