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A179291
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Greatest k <= n such that 2^n+2^k-1 is prime, or 0 if no such k exists.
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3
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1, 2, 2, 4, 4, 6, 6, 7, 0, 8, 6, 12, 8, 12, 10, 16, 0, 18, 18, 18, 12, 10, 16, 21, 0, 15, 22, 22, 0, 30, 20, 24, 0, 32, 34, 21, 8, 3, 38, 36, 16, 26, 0, 43, 0, 43, 42, 43, 0, 48, 46, 38, 0, 28, 44, 55, 0, 54, 0, 60, 56, 28, 56, 60, 64, 63, 48, 60, 0
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OFFSET
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1,2
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COMMENTS
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Up to n=6600, a(n) = 0 for 867 values of n and a(n) >= n/2 for 4931 values of n.
When n+1 is a prime in A000043 and k=n, then 2^n+2^k-1 = 2^(n+1)-1 is a Mersenne Prime.
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LINKS
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MATHEMATICA
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Table[k=n; While[k>0 && ! PrimeQ[2^n+2^k-1], k--]; k, {n, 100}] (* T. D. Noe, Jan 12 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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