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.

3, 5, 6, 7, 10, 12, 14, 17, 20, 24, 28, 31, 34, 40, 48, 56, 62, 68, 80, 96, 112, 124, 127, 136, 160, 192, 224, 248, 254, 257, 272, 320, 384, 448, 496, 508, 514, 544, 640, 768, 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

Offset: 1

Author

Antti Karttunen, Jun 30 2020

Keywords

• nonn

Comments

Numbers k such that A000265(k) is either in A000668 or in A019434.

Product of any two terms (whether distinct or not) can be found in A335912.

Crossrefs

Row 1 of A335910.

Union of A334101 and A335431. Subsequence of A038550.

Cf. A000668, A000668, A335885, A335912.

Cf. A141453 (after its initial 2, gives the primes present in this sequence).

Programs

PARI

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))))); };
isA335911(n) = (1==A335885(n));

PARI

A000265(n) = (n>>valuation(n,2));
isA000668(n) = (isprime(n)&&!bitand(n,1+n));
isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2, n-1));
isA335911(n) = (isA000668(A000265(n))||isA019434(A000265(n)));