A232747 Inverse function to Hofstadter's A005228.

1, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0

Offset: 1

Author

Antti Karttunen, Nov 30 2013

Keywords

• nonn

Comments

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

Note that a(n)*A232749(n) = 0 for all n.

Used to compute the permutation A232751.

Links

• Index entries for Hofstadter-type sequences

Crossrefs

A030124 gives the positions of zeros.

Cf. A005228, A232746, A232749, 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]]];
a[n_] := If[n == 1, 1, a46[n] (a46[n] - a46[n - 1])];
Array[a, nmax] (* Jean-François Alcover, Dec 09 2021 *)

Formula

a(1)=1, and for n>1, a(n) = A232746(n) * (A232746(n)-A232746(n-1)).