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A239638
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Numbers n such that the semiprime 2^n-1 is divisible by 2n+1.
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1
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OFFSET
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1,1
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COMMENTS
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All terms are primes == 5 modulo 6 (A005384 Sophie Germain primes).
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LINKS
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EXAMPLE
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n = 11, 2^n -1 = 2047 = 23*89,
n = 23, 8388607 = 47*178481,
n = 131, 2722258935367507707706996859454145691647 = 263*10350794431055162386718619237468234569.
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MATHEMATICA
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Select[Range[4000], PrimeQ[2*# + 1] && PowerMod[2, #, 2*# + 1] == 1 &&
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PROG
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(PARI) is(n)=n%6==5 && Mod(2, 2*n+1)^n==1 && isprime(2*n+1) && ispseudoprime((2^n-1)/(2*n+1)) \\ Charles R Greathouse IV, Aug 25 2016
(Python)
from sympy import isprime, nextprime
while p < 10**6:
if (p % 6) == 5:
n = (p-1)//2
if pow(2, n, p) == 1 and isprime((2**n-1)//p):
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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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