A326674 GCD of the set of positions of 1's in the reversed binary expansion of n.

1, 2, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

a(n) is even if and only if n is in A062880. - Robert Israel, Oct 13 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Trivially, a(n) <= log_2(n). - Charles R Greathouse IV, Nov 15 2022

Example

The reversed binary expansion of 40 is (0,0,0,1,0,1), with positions of 1's being {4,6}, so a(40) = GCD(4,6) = 2.

Maple

f:= proc(n) local B;
  B:= convert(n, base, 2);
  igcd(op(select(t -> B[t]=1, [$1..ilog2(n)+1])))
end proc:
map(f, [$1..100]); # Robert Israel, Oct 13 2020

Mathematica

Table[GCD@@Join@@Position[Reverse[IntegerDigits[n, 2]], 1], {n, 100}]

Crossrefs

Positions of 1's are A291166, and non-1's are A291165.

GCDs of prime indices are A289508.

GCDs of strict partitions encoded by FDH numbers are A319826.

Numbers whose binary positions are pairwise coprime are A326675.

Cf. A000120, A051293, A062880, A070939, A326667, A326668, A326669, A326670, A326672, A326673.

Sequence in context: A006083 A338713 A080301 * A331184 A333768 A306922

Adjacent sequences: A326671 A326672 A326673 * A326675 A326676 A326677

Keyword

nonn,base

Author

Gus Wiseman, Jul 17 2019

Status

approved