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A234016 Partial sums of the characteristic function of A055938. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

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))>0: 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.

Sequence in context: A039728 A332965 A334220 * A029119 A178042 A308950

Adjacent sequences:  A234013 A234014 A234015 * A234017 A234018 A234019

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 18 2013

STATUS

approved

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Last modified January 28 05:01 EST 2021. Contains 340490 sequences. (Running on oeis4.)