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

Author

Antti Karttunen, Dec 18 2013

Keywords

• nonn

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

Crossrefs

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

Programs

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

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].