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A276495
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Odd numbers not of the form p + 2^m with p prime and m >= 0 for which the smallest k in A067760 such that n + 2^k is prime increases.
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1
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1, 127, 251, 1657, 1777, 1973, 3181, 21893, 31951, 50839, 67607, 138977
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OFFSET
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1,2
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COMMENTS
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There exist de Polignac numbers n such that for all k >= 1 the numbers n + 2^k are composite. It is conjectured that 30666137 is the smallest such number.
a(13) >= 453143.
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LINKS
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PROG
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(Magma) lst:=[]; c:=0; for n in [1..31951 by 2] do m:=-1; repeat m+:=1; a:=n-2^m; until a lt 1 or IsPrime(a); if a lt 1 then k:=0; repeat k+:=1; b:=n+2^k; until IsPrime(b); if k gt c then Append(~lst, n); c:=k; end if; end if; end for; lst;
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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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STATUS
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approved
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