A326032 a(2^x + ... + 2^z) = w(x) + ... + w(z), where x...z are distinct nonnegative integers and w = A000120.

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 3, 3, 4, 4, 4, 4, 5

Offset: 0

Author

Gus Wiseman, Jul 22 2019

Keywords

• nonn

Comments

From Robert Israel, Jul 23 2019: (Start)

a(2*n+1)=a(2*n).

a(n)=1 if and only if n > 1 is in A283526. (End)

Examples

			For example, a(6) = a(2^2 + 2^1) = w(2) + w(1) = 2.
		

Crossrefs

Other sequences that are built by replacing 2^k in the binary representation with other numbers: A022290 (Fibonacci), A059590 (factorials), A073642, A089625 (primes), A116549, A326031.

Cf. A000120, A029931, A035327, A048793, A070939, A283526, A305830, A326031, A326669, A326702.

Programs

Maple

Bwt:= proc(n) option remember; convert(convert(n,base,2),`+`) end proc:
f:= proc(n) local L,i;
  L:= convert(n,base,2);
  add(L[i]*Bwt(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Jul 23 2019

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
Table[Total[Length/@bpe/@(bpe[n]-1)],{n,0,100}]