A232748 - OEIS

%I #11 Dec 09 2021 03:23:24

%S 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,

%T 22,23,24,25,26,27,28,28,29,30,31,32,33,34,35,36,37,37,38,39,40,41,42,

%U 43,44,45,46,47,47,48,49,50,51,52,53,54,55,56,57,58,59

%N Partial sums of the characteristic function of Hofstadter's A030124.

%C Useful for computing A232749.

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

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

%t nmax = 100; A5228 = {1}; Module[{d = 2, k = 1}, Do[While[MemberQ[A5228, d], d++]; k += d; d++; AppendTo[A5228, k], {n, 1, nmax}]];

%t a46[n_] := For[k = 1, True, k++, If[A5228[[k]] > n, Return[k-1]]];

%t a[n_] := a[n] = If[n == 1, 0, a[n-1] + (1 - (a46[n] - a46[n-1]))];

%t Array[a, nmax] (* _Jean-François Alcover_, Dec 09 2021 *)

%o (Scheme, with memoization macro definec from _Antti Karttunen_'s IntSeq-library)

%o (definec (A232748 n) (cond ((< n 2) (- n 1)) (else (+ (A232748 (- n 1)) (- 1 (- (A232746 n) (A232746 (- n 1))))))))

%Y Cf. A030124, A232746, A232749.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 30 2013