A348340 For n >= 1; x = n, then iterate x --> x + h(x) until h(x + h(x)) >= h(x). a(n) gives the number of iteration steps where h(i) is A000120(i).

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

Offset: 1

Author

Ctibor O. Zizka, Oct 13 2021

Keywords

• nonn
• base

Comments

a(n) = 1 for n such that A000120(n + A000120(n)) < A000120(n).

Examples

			n = 19; x(1) = 19 + h(19) = 22, h(22) >= h(19) thus x(2) = 22 + h(22) = 25, h(25) >= h(22) thus x(3) = 25 + h(25) = 28, h(28) >= h(25) thus x(4) = 28 + h(28) = 31, h(31) >= h(28) thus x(5) =  31 + h(31) = 36, h(36) < h(31) thus stop. a(19) = 5. h(i) is A000120(i).
		

Crossrefs

Cf. A000120, A092391.

Programs

Mathematica

h[n_] := DigitCount[n, 2, 1]; x[n_] := n + h[n]; a[n_] := Length@ NestWhileList[x, n, h[#] <= h[x[#]] &]; Array[a, 110] (* Amiram Eldar, Oct 15 2021 *)