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A263046
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Smallest number k>2 such that k*2^n + 1 is a prime number.
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1
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4, 3, 3, 5, 6, 3, 3, 5, 3, 15, 12, 6, 3, 5, 4, 5, 12, 6, 3, 11, 7, 11, 25, 20, 10, 5, 7, 15, 12, 6, 3, 35, 18, 9, 12, 6, 3, 15, 10, 5, 6, 3, 9, 9, 15, 35, 19, 27, 15, 14, 7, 14, 7, 20, 10, 5, 27, 29, 54, 27, 31, 36, 18, 9, 12, 6, 3, 9, 31, 23, 39, 39, 40, 20, 10, 5, 58
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OFFSET
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0,1
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COMMENTS
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If k = 2^j then 2^(n+j) + 1 is a Fermat prime.
a(n) = 3 if and only if 3*2^n + 1 is a prime; that is, n belongs to A002253. - Altug Alkan, Oct 08 2015
a(n+1) >= ceiling(a(n)/2). If a(n) is even then a(n+1) = a(n)/2. - Robert Israel, Oct 08 2015
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LINKS
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EXAMPLE
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3*2^1 + 1 = 7 (prime), so a(1)=3:
3*2^2 + 1 = 13 (prime), so a(2)=3;
3*2^3 + 1 = 25 (composite), 4*2^3 + 1 = 33 (composite), 5*2^3 - 1 = 41 (prime), so a(3)=5.
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MAPLE
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f:= proc(n) local k;
for k from 3 do if isprime(k*2^n+1) then return k fi od
end proc:
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MATHEMATICA
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Table[k = 3; While[! PrimeQ[k 2^n + 1], k++]; k, {n, 76}] (* Michael De Vlieger, Oct 08 2015 *)
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PROG
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(PARI) a(n) = {k=3; while (! isprime(k*2^n+1), k++); k; } \\ Michel Marcus, Oct 08 2015
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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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