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A067526
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Numbers n such that n - 2^k is a prime or 1 for all k satisfying 0 < k, 2^k < n.
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6
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OFFSET
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1,1
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COMMENTS
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Is the sequence finite?
Next term, if it exists, exceeds 5*10^9. - Sean A. Irvine, Dec 18 2023
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LINKS
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EXAMPLE
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45 belongs to this sequence as 45-2, 45-4, 45-8, 45-16, 45-32, i.e., 43, 41, 37, 29 and 13 are all primes.
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[2^k < n, k++ ]; k--; k]; Do[ a = Table[n - 2^k, {k, 1, f[n]} ]; If[ a[[ -1]] == 1, a = Drop[a, -1]]; If[ Union[ PrimeQ[a]] == {True}, Print[n]], {n, 5, 10^7, 2} ]
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PROG
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(Python)
from sympy import isprime
def ok(n):
k, pow2 = 1, 2
while pow2 < n - 1:
if not isprime(n-pow2): return False
pow2 *= 2
return (2 < n)
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CROSSREFS
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KEYWORD
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nonn,hard,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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