A232748 Partial sums of the characteristic function of Hofstadter's A030124.

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

Offset: 1

Author

Antti Karttunen, Nov 30 2013

Keywords

• nonn

Comments

Useful for computing A232749.

Links

• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A030124, A232746, A232749.

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_] := a[n] = If[n == 1, 0, a[n-1] + (1 - (a46[n] - a46[n-1]))];
Array[a, nmax] (* Jean-François Alcover, Dec 09 2021 *)

Formula

a(1)=0, and for n>1, a(n) = A232748(n-1) + (1-(A232746(n)-A232746(n-1))).