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

1,4

Comments

Useful for computing A232749.

Links

Table of n, a(n) for n=1..68.

Index entries for Hofstadter-type sequences

Formula

a(1)=0, and for n>1, a(n) = A232748(n-1) + (1-(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_] := a[n] = If[n == 1, 0, a[n-1] + (1 - (a46[n] - a46[n-1]))];
Array[a, nmax] (* Jean-François Alcover, Dec 09 2021 *)

Prog

(Scheme, with memoization macro definec from Antti Karttunen's IntSeq-library)
(definec (A232748 n) (cond ((< n 2) (- n 1)) (else (+ (A232748 (- n 1)) (- 1 (- (A232746 n) (A232746 (- n 1))))))))

Crossrefs

Cf. A030124, A232746, A232749.

Sequence in context: A090223 A366870 A171974 * A308936 A187737 A109401

Adjacent sequences: A232745 A232746 A232747 * A232749 A232750 A232751

Keyword

nonn

Author

Antti Karttunen, Nov 30 2013

Status

approved