A343299 a(n) = n + A000120(a(n-1)) - a(n-1), with n > 1, a(1) = 1, where A000120(x) is the binary weight of x.

1, 2, 2, 3, 4, 3, 6, 4, 6, 6, 7, 8, 6, 10, 7, 12, 7, 14, 8, 13, 11, 14, 12, 14, 14, 15, 16, 13, 19, 14, 20, 14, 22, 15, 24, 14, 26, 15, 28, 15, 30, 16, 28, 19, 29, 21, 29, 23, 30, 24, 29, 27, 30, 28, 30, 30, 31, 32

Offset: 1

Author

Clément Vovard, Apr 11 2021

Keywords

• base
• look
• nonn

Comments

The 'crossings' that appear in the graph seem to occur when a(n) is a power of 2.

Examples

			a(2) = 2 + A000120(1) - 1 = 2 + 1 - 1 = 2.
a(6) = 6 + A000120(4) - 4 = 6 + 1 - 4 = 3.
		

Links

• Clément Vovard, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Log-log scatterplot of a(n) for n = 1..2^16.
• Michael De Vlieger, Log-log scatterplot of a(n) for n = 1..2^10 with color function registering binary weight of a(n-1).
• Michael De Vlieger, Log-log scatterplot of a(n) for n = 1..2^10 with even n in red and odd n in blue.

Crossrefs

Cf. A000120, A011371

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = n + DigitCount[a[n - 1], 2, 1] - a[n - 1]; Array[a, 100] (* Amiram Eldar, Apr 12 2021 *)

PARI

lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = n + hammingweight(va[n-1]) - va[n-1];); va;} \\ Michel Marcus, Apr 12 2021

Formula

a(n) = n - A011371(a(n-1)).