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%I #23 Mar 13 2018 22:14:40
%S 7,11,23,41,47,59,83,89,97,107,137,167,179,227,233,263,347,353,359,
%T 383,467,479,503,563,569,587,641,719,809,839,857,863,887,929,983,1019,
%U 1049,1097,1187,1193,1283,1307,1319,1367,1409,1433,1439,1487,1523,1619,1697
%N Primes of the form p*2^k + 1, where p is an odd prime and k is odd.
%C 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.
%C This conjecture has been verified for n up to 10^10.
%H Robert Israel, <a href="/A294074/b294074.txt">Table of n, a(n) for n = 1..10000</a>
%p 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:
%p select(filter, [seq(n,n=3..2000,2)]); # _Robert Israel_, Mar 13 2018
%t 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
%o (PARI) isok(p) = isprime(p) && (pp=p-1) && (v=valuation(pp,2)) && (v%2) && isprime(pp/2^v); \\ _Michel Marcus_, Feb 09 2018
%Y Subsequence of A058500.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Feb 07 2018
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