A334101 Numbers of the form q*(2^k), where q is one of the Fermat primes and k >= 0; Numbers n for which A329697(n) == 1.

3, 5, 6, 10, 12, 17, 20, 24, 34, 40, 48, 68, 80, 96, 136, 160, 192, 257, 272, 320, 384, 514, 544, 640, 768, 1028, 1088, 1280, 1536, 2056, 2176, 2560, 3072, 4112, 4352, 5120, 6144, 8224, 8704, 10240, 12288, 16448, 17408, 20480, 24576, 32896, 34816, 40960, 49152, 65537, 65792, 69632, 81920, 98304, 131074, 131584, 139264

Offset

1,1

Comments

Numbers k that themselves are not powers of two, but for which A171462(k) = k-A052126(k) is [a power of 2].

Numbers k such that A000265(k) is in A019434.

Squares of these numbers can be found (as a subset) in A334102, and the cubes (as a subset) in A334103.

Links

Table of n, a(n) for n=1..57.

Formula

For all n, A000120(a(n)) = 2.

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2, n-1));
isA334101(n) = isA019434(A000265(n));
(PARI)
A052126(n) = if(1==n, n, n/vecmax(factor(n)[, 1]));
A209229(n) = (n && !bitand(n, n-1));
isA334101(n) = ((!A209229(n))&&A209229(n-A052126(n)));

Crossrefs

Row 1 of A334100.

Cf. A000120, A000265, A052126, A171462, A209229, A329697, A334102, A334103.

Cf. A019434 (primes present), A007283, A020714, A110287 (other subsequences).

Subsequence of A018900.

Sequence in context: A207063 A359584 A230851 * A265749 A115823 A190721

Adjacent sequences: A334098 A334099 A334100 * A334102 A334103 A334104

Keyword

nonn

Author

Antti Karttunen, Apr 14 2020

Status

approved