A234016 Partial sums of the characteristic function of A055938.

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, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 19, 20, 21, 22, 22, 22, 23, 23, 23, 24, 25, 25, 25, 26, 26, 26, 27, 28, 29, 30, 31, 31, 31, 32, 32, 32, 33, 34

Offset

0,6

Comments

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

Conjecture: partial sums of A308187 (i.e, A308187 is the characteristic function of A055938). - Sean A. Irvine, Jul 16 2022

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Formula

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

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

Prog

(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)
(definec (A234016 n) (if (< n 2) 0 (+ (A234016 (- n 1)) (- 1 (A079559 n)))))
;; Alternatively, based on A046699, with its October 2012 starting offset:
(define (A234016 n) (- n (- (A046699 (+ n 2)) 1)))
(Python)
from sympy import factorial
def a046699(n):
    if n<3: return 1
    s=1
    while factorial(2*s)%(2**(n - 1)): s+=1
    return s
def a(n): return n - (a046699(n + 2) - 1)
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 11 2017

Crossrefs

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

Sequence in context: A332965 A354779 A334220 * A029119 A178042 A308950

Adjacent sequences: A234013 A234014 A234015 * A234017 A234018 A234019

Keyword

nonn

Author

Antti Karttunen, Dec 18 2013

Status

approved