A355807 a(n) is the number at the apex of a triangle whose base contains the distinct powers of 2 summing to n (in ascending order), and each number in a higher row is the absolute difference of the two numbers directly below it; a(0) = 0.

0, 1, 2, 1, 4, 3, 2, 1, 8, 7, 6, 5, 4, 1, 2, 1, 16, 15, 14, 13, 12, 9, 10, 9, 8, 1, 2, 3, 4, 3, 2, 1, 32, 31, 30, 29, 28, 25, 26, 25, 24, 17, 18, 13, 20, 19, 18, 17, 16, 1, 2, 11, 4, 5, 6, 3, 8, 7, 6, 3, 4, 1, 2, 1, 64, 63, 62, 61, 60, 57, 58, 57, 56, 49, 50

Offset

0,3

Comments

This sequence has similarities with A334387.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

a(n) <= n with equality iff n = 0 or n is a power of 2.

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

Example

For n = 27:
- we have the following triangle:
            3
          5   2
        1   6   8
      1   2   8  16
- so a(27) = 3.

Prog

(PARI) a(n) = { my (b=vector(hammingweight(n))); for (k=1, #b, n-=b[k]=2^valuation(n, 2)); while (#b>1, b=vector(#b-1, k, abs(b[k+1]-b[k]))); if (#b, b[1], 0) }

Crossrefs

See A355808, A355809, A355810 and A355811 for other variants.

Cf. A133457, A334387, A348296.

Sequence in context: A281589 A302436 A283167 * A355808 A080079 A341707

Adjacent sequences: A355804 A355805 A355806 * A355808 A355809 A355810

Keyword

nonn,base

Author

Rémy Sigrist, Jul 18 2022

Status

approved