login
Partial sums of the characteristic function of A055938.
5

%I #22 Jul 16 2022 00:54:34

%S 0,0,1,1,1,2,3,3,3,4,4,4,5,6,7,7,7,8,8,8,9,10,10,10,11,11,11,12,13,14,

%T 15,15,15,16,16,16,17,18,18,18,19,19,19,20,21,22,22,22,23,23,23,24,25,

%U 25,25,26,26,26,27,28,29,30,31,31,31,32,32,32,33,34

%N Partial sums of the characteristic function of A055938.

%C Also: a(0) = a(1) = 0, and thereafter, a(n) = the largest k such that A055938(k) <= n.

%C Conjecture: partial sums of A308187 (i.e, A308187 is the characteristic function of A055938). - _Sean A. Irvine_, Jul 16 2022

%H Antti Karttunen, <a href="/A234016/b234016.txt">Table of n, a(n) for n = 0..8191</a>

%F If n < 2, a(n)=0, otherwise a(n) = a(n-1) + (1-A079559(n)).

%F a(n) = n - (A046699(n+2)-1) [With A046699's October 2012 starting offset].

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

%o (definec (A234016 n) (if (< n 2) 0 (+ (A234016 (- n 1)) (- 1 (A079559 n)))))

%o ;; Alternatively, based on A046699, with its October 2012 starting offset:

%o (define (A234016 n) (- n (- (A046699 (+ n 2)) 1)))

%o (Python)

%o from sympy import factorial

%o def a046699(n):

%o if n<3: return 1

%o s=1

%o while factorial(2*s)%(2**(n - 1)): s+=1

%o return s

%o def a(n): return n - (a046699(n + 2) - 1)

%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 11 2017

%Y Cf. A046699, A055938, A079559, A234017, A233275, A308187.

%K nonn

%O 0,6

%A _Antti Karttunen_, Dec 18 2013