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A294074
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Primes of the form p*2^k + 1, where p is an odd prime and k is odd.
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1
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7, 11, 23, 41, 47, 59, 83, 89, 97, 107, 137, 167, 179, 227, 233, 263, 347, 353, 359, 383, 467, 479, 503, 563, 569, 587, 641, 719, 809, 839, 857, 863, 887, 929, 983, 1019, 1049, 1097, 1187, 1193, 1283, 1307, 1319, 1367, 1409, 1433, 1439, 1487, 1523, 1619, 1697
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OFFSET
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1,1
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COMMENTS
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I conjecture that a number of the form p*2^k + 1 (with odd prime p and odd k) belongs to this sequence if and only if p*2^k + 1 divides (p + 2)^(p*2^k) - 1.
This conjecture has been verified for n up to 10^10.
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LINKS
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MAPLE
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filter:= proc(n) local k; if not isprime(n) then return false fi; k:= padic:-ordp(n-1, 2); k::odd and isprime((n-1)/2^k) end proc:
select(filter, [seq(n, n=3..2000, 2)]); # Robert Israel, Mar 13 2018
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MATHEMATICA
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lst = {}; Do[v = IntegerExponent[m - 1, 2]; If[OddQ[v], If[PrimeQ[(m - 1)/2^v] && PrimeQ[m], AppendTo[lst, m]]], {m, 3, 1697, 2}]; lst
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PROG
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(PARI) isok(p) = isprime(p) && (pp=p-1) && (v=valuation(pp, 2)) && (v%2) && isprime(pp/2^v); \\ Michel Marcus, Feb 09 2018
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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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