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

1,4

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

Table of n, a(n) for n=1..70.

Index entries for Hofstadter-type sequences

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 *)

Prog

(Scheme, with memoization macro definec from Antti Karttunen's IntSeq-library)
(definec (A232749 n) (cond ((< n 2) 0) (else (* (A232748 n) (- (A232748 n) (A232748 (- n 1)))))))

Crossrefs

A005228 gives the positions of zeros.

Cf. A030124, A232747, A232748, A232751.

Sequence in context: A119974 A195828 A322981 * A181578 A065332 A378212

Adjacent sequences: A232746 A232747 A232748 * A232750 A232751 A232752

Keyword

nonn

Author

Antti Karttunen, Nov 30 2013

Status

approved