

A294074


Primes of the form p*2^k + 1, where p is an odd prime and k is odd.


1



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

1,1


COMMENTS

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.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


MAPLE

filter:= proc(n) local k; if not isprime(n) then return false fi; k:= padic:ordp(n1, 2); k::odd and isprime((n1)/2^k) end proc:
select(filter, [seq(n, n=3..2000, 2)]); # Robert Israel, Mar 13 2018


MATHEMATICA

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


PROG

(PARI) isok(p) = isprime(p) && (pp=p1) && (v=valuation(pp, 2)) && (v%2) && isprime(pp/2^v); \\ Michel Marcus, Feb 09 2018


CROSSREFS

Subsequence of A058500.
Sequence in context: A239733 A265768 A210001 * A228227 A107133 A079138
Adjacent sequences: A294071 A294072 A294073 * A294075 A294076 A294077


KEYWORD

nonn


AUTHOR

Arkadiusz Wesolowski, Feb 07 2018


STATUS

approved



