A309776 Form a triangle: first row is n in base 2, next row is sums of pairs of adjacent digits of previous row, repeat until get a single number which is a(n).

0, 1, 1, 2, 1, 2, 3, 4, 1, 2, 4, 5, 4, 5, 7, 8, 1, 2, 5, 6, 7, 8, 11, 12, 5, 6, 9, 10, 11, 12, 15, 16, 1, 2, 6, 7, 11, 12, 16, 17, 11, 12, 16, 17, 21, 22, 26, 27, 6, 7, 11, 12, 16, 17, 21, 22, 16, 17, 21, 22, 26, 27, 31, 32, 1, 2, 7, 8, 16, 17, 22, 23, 21, 22

Offset

0,4

Comments

a(n) = 1 occurs at n = 2^k for nonnegative integers k.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Formula

From Bernard Schott, Sep 22 2019: (Start)

a(2^k + 1) = 2 for k >= 1 where 2^k+1 = 1000..0001_2.

a(2^k - 1) = 2^(k-1) for k >= 2 where 2^k-1 = 111..111_2.

a((4^k-1)/3) = 2^(2*k-3) for k >= 2 where (4^k-1)/3 = 10101..0101_2.

(End)

Example

For n=5 the triangle is
  1 0 1
   1 1
    2
so a(5)=2.
For n=14 we get
  1 1 1 0
   2 2 1
    4 3
     7
so a(14)=7.
For n=26=11010_2; (n1+n2, n2+n3, n3+n4, n4+n5) = 2111; (n1'+n2', n2'+n3', n3'+n4') = 322; (n1''+n2'', n2''+n3'') = 54; (n1'''+n2''') = 9; a(26)= 9.

Prog

(PARI) a(n) = my (b=binary(n)); sum(k=1, #b, b[k]*binomial(#b-1, k-1)) \\ Rémy Sigrist, Aug 20 2019

Crossrefs

Cf. A306607.

Sequence in context: A233782 A233972 A169778 * A255560 A328472 A046653

Adjacent sequences: A309773 A309774 A309775 * A309777 A309778 A309779

Keyword

nonn,base

Author

Cameron Musard, Aug 16 2019

Extensions

Edited by N. J. A. Sloane, Sep 21 2019

Data corrected by Rémy Sigrist, Sep 22 2019

Status

approved