cp's OEIS Frontend

A335911 Numbers of the form q*(2^k), where k >= 0 and q is either a Fermat prime or a Mersenne prime; Numbers k for which A335885(k) = 1.

%I A335911 #9 Jul 09 2020 22:38:25
%S A335911 3,5,6,7,10,12,14,17,20,24,28,31,34,40,48,56,62,68,80,96,112,124,127,
%T A335911 136,160,192,224,248,254,257,272,320,384,448,496,508,514,544,640,768,
%U A335911 896,992,1016,1028,1088,1280,1536,1792,1984,2032,2056,2176,2560,3072,3584,3968,4064,4112,4352,5120,6144,7168,7936,8128,8191
%N A335911 Numbers of the form q*(2^k), where k >= 0 and q is either a Fermat prime or a Mersenne prime; Numbers k for which A335885(k) = 1.
%C A335911 Numbers k such that A000265(k) is either in A000668 or in A019434.
%C A335911 Product of any two terms (whether distinct or not) can be found in A335912.
%o A335911 (PARI)
%o A335911 A335885(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+min(A335885(f[k,1]-1),A335885(f[k,1]+1))))); };
%o A335911 isA335911(n) = (1==A335885(n));
%o A335911 (PARI)
%o A335911 A000265(n) = (n>>valuation(n,2));
%o A335911 isA000668(n) = (isprime(n)&&!bitand(n,1+n));
%o A335911 isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2, n-1));
%o A335911 isA335911(n) = (isA000668(A000265(n))||isA019434(A000265(n)));
%Y A335911 Row 1 of A335910.
%Y A335911 Union of A334101 and A335431. Subsequence of A038550.
%Y A335911 Cf. A000668, A000668, A335885, A335912.
%Y A335911 Cf. A141453 (after its initial 2, gives the primes present in this sequence).
%K A335911 nonn
%O A335911 1,1
%A A335911 _Antti Karttunen_, Jun 30 2020