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

1,1

Comments

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

Links

Table of n, a(n) for n=1..110.

Example

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).

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 *)

Crossrefs

Cf. A000120, A092391.

Sequence in context: A132669 A276052 A374420 * A321028 A351169 A263356

Adjacent sequences: A348337 A348338 A348339 * A348341 A348342 A348343

Keyword

nonn,base

Author

Ctibor O. Zizka, Oct 13 2021

Status

approved