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

1,3

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

Table of n, a(n) for n=1..86.

Index entries for Hofstadter-type sequences

Formula

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

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(definec (A232747 n) (cond ((< n 2) n) (else (* (A232746 n) (- (A232746 n) (A232746 (- n 1)))))))

Crossrefs

A030124 gives the positions of zeros.

Cf. A005228, A232746, A232749, A232751.

Sequence in context: A284273 A083927 A154724 * A130460 A132440 A218272

Adjacent sequences: A232744 A232745 A232746 * A232748 A232749 A232750

Keyword

nonn

Author

Antti Karttunen, Nov 30 2013

Status

approved