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A274589 Primes not of the form (prime+1)*2^k-1 with k>=1.

%I A274589 #10 Jul 02 2016 02:08:14
%S A274589 2,3,13,17,19,29,37,41,43,53,61,67,73,89,97,101,103,109,113,131,137,
%T A274589 139,149,157,163,173,181,193,197,199,211,229,233,241,251,257,269,277,
%U A274589 281,283,293,307,311,313,317,331,337,349,353,367
%N A274589 Primes not of the form (prime+1)*2^k-1 with k>=1.
%C A274589 A permutation of A057026 (excluding the zeros, e.g., A057026(254601) = 0).
%H A274589 Robert Israel, <a href="/A274589/b274589.txt">Table of n, a(n) for n = 1..10000</a>
%e A274589 103 = (51+1)*2^1-1 = (25+1)*2^2-1 = (12+1)*2^3-1, the numbers 51, 25 and 12 are not primes, so 103 is in the sequence.
%e A274589 71 = (35+1)*2^1-1 = (17+1)*2^2-1 = (8+1)*2^3-1, the number 17 is prime, so 71 is not in the sequence.
%p A274589 filter := proc(n) local k;
%p A274589   if not isprime(n) then return false fi;
%p A274589   for k from 1 to padic:-ordp(n+1,2) do
%p A274589      if isprime((n+1)/2^k-1) then return false
%p A274589      fi
%p A274589   od:
%p A274589   true
%p A274589 end proc:
%p A274589 select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Jun 29 2016
%Y A274589 Cf. A057026, A266233 (complement with respect to A000040).
%K A274589 nonn
%O A274589 1,1
%A A274589 _Gionata Neri_, Jun 29 2016