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A276417
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a(n) = least positive k such that (2*n + 1) - 2^k is prime, or 0 if no such k exists.
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2
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0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 4, 1, 2, 4, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 4, 1, 2, 4, 3, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 3, 4, 4, 0, 1, 2, 1, 2, 6, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 1, 2, 5, 1, 2, 1, 2, 4
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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If A188903(n) >= 2, then a(n) = log_2(A188903(n)), otherwise a(n) = 0.
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EXAMPLE
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a(14) = 4 because (2*14 + 1) - 2^k is composite for k = 1, 2, 3 and prime for k = 4.
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MAPLE
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f:= proc(n) local k;
for k from 1 do
if 2*n < 2^k then return 0
elif isprime(2*n+1-2^k) then return k
fi
od
end proc:
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MATHEMATICA
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Table[If[n <= 2, 0, k = 1; While[! PrimeQ[2 n + 1 - 2^k], k++]; k], {n, 0, 120}] (* Michael De Vlieger, Sep 03 2016 *)
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PROG
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(Magma) lst:=[]; for n in [1..173 by 2] do k:=0; c:=k; repeat k+:=1; c+:=1; a:=n-2^k; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, 0); else Append(~lst, c); end if; end for; lst;
(PARI) a(n) = my(k=1); while(2^k < 2*n+1, if(ispseudoprime((2*n+1)-2^k), return(k)); k++); return(0) \\ Felix Fröhlich, Sep 02 2016
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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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