A355810 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 bitwise XOR of the two numbers directly below it; a(0) = 0.

0, 1, 2, 3, 4, 5, 6, 5, 8, 9, 10, 9, 12, 9, 10, 15, 16, 17, 18, 17, 20, 17, 18, 23, 24, 17, 18, 27, 20, 29, 30, 17, 32, 33, 34, 33, 36, 33, 34, 39, 40, 33, 34, 43, 36, 45, 46, 33, 48, 33, 34, 51, 36, 53, 54, 33, 40, 57, 58, 33, 60, 33, 34, 51, 64, 65, 66, 65

Offset: 0

Author

Rémy Sigrist, Jul 18 2022

Keywords

• nonn
• base

Examples

			For n = 27:
- we have the following triangle:
          27
         9  18
       3  10  24
     1   2   8  16
- so a(27) = 27.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

See A355807 for similar sequences.

Cf. A143071, A348296.

Programs

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, bitxor(b[k+1], b[k]))); if (#b, b[1], 0) }

Formula

a(n) <= n with equality iff n = 0 or n belongs to A143071.

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