A232749 Inverse function to Hofstadter's A030124.

0, 1, 0, 2, 3, 4, 0, 5, 6, 7, 8, 0, 9, 10, 11, 12, 13, 0, 14, 15, 16, 17, 18, 19, 20, 0, 21, 22, 23, 24, 25, 26, 27, 28, 0, 29, 30, 31, 32, 33, 34, 35, 36, 37, 0, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 0, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 0, 60

Offset: 1

Author

Antti Karttunen, Nov 30 2013

Keywords

• nonn

Comments

This is an inverse function for Hofstadter's A030124 in the sense that for all n, n = a(A030124(n)). a(n) = 0 when n is not in A030124, but instead in its complement A005228.

Note that A232747(n)*a(n) = 0 for all n.

Used to compute the permutation A232751.

Links

• Index entries for Hofstadter-type sequences

Crossrefs

A005228 gives the positions of zeros.

Cf. A030124, A232747, A232748, A232751.

Programs

Mathematica

nmax = 100; A5228 = {1};
Module[{d = 2, k = 1}, Do[While[MemberQ[A5228, d], d++];
     k += d; d++; AppendTo[A5228, k], {n, 1, nmax}]];
a46[n_] := For[k = 1, True, k++, If[A5228[[k]] > n, Return[k - 1]]];
a48[n_] := a48[n] = If[n == 1, 0, a48[n-1] + (1 - (a46[n] - a46[n - 1]))];
a[n_] := If[n == 1, 0, a48[n] (a48[n] - a48[n - 1])];
Array[a, nmax] (* Jean-François Alcover, Dec 09 2021 *)