cp's OEIS Frontend

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.

%I A334101 #16 Apr 16 2020 18:49:35
%S A334101 3,5,6,10,12,17,20,24,34,40,48,68,80,96,136,160,192,257,272,320,384,
%T A334101 514,544,640,768,1028,1088,1280,1536,2056,2176,2560,3072,4112,4352,
%U A334101 5120,6144,8224,8704,10240,12288,16448,17408,20480,24576,32896,34816,40960,49152,65537,65792,69632,81920,98304,131074,131584,139264
%N 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.
%C A334101 Numbers k that themselves are not powers of two, but for which A171462(k) = k-A052126(k) is [a power of 2].
%C A334101 Numbers k such that A000265(k) is in A019434.
%C A334101 Squares of these numbers can be found (as a subset) in A334102, and the cubes (as a subset) in A334103.
%F A334101 For all n, A000120(a(n)) = 2.
%o A334101 (PARI)
%o A334101 A000265(n) = (n>>valuation(n,2));
%o A334101 isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2,n-1));
%o A334101 isA334101(n) = isA019434(A000265(n));
%o A334101 (PARI)
%o A334101 A052126(n) = if(1==n,n,n/vecmax(factor(n)[, 1]));
%o A334101 A209229(n) = (n && !bitand(n,n-1));
%o A334101 isA334101(n) = ((!A209229(n))&&A209229(n-A052126(n)));
%Y A334101 Row 1 of A334100.
%Y A334101 Cf. A000120, A000265, A052126, A171462, A209229, A329697, A334102, A334103.
%Y A334101 Cf. A019434 (primes present), A007283, A020714, A110287 (other subsequences).
%Y A334101 Subsequence of A018900.
%K A334101 nonn
%O A334101 1,1
%A A334101 _Antti Karttunen_, Apr 14 2020