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A234016
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Partial sums of the characteristic function of A055938.
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5
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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
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OFFSET
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0,6
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COMMENTS
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Also: a(0) = a(1) = 0, and thereafter, a(n) = the largest k such that A055938(k) <= n.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 0..8191
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FORMULA
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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].
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PROG
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(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
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CROSSREFS
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Cf. A046699, A055938, A079559, A234017, A233275.
Sequence in context: A039728 A332965 A334220 * A029119 A178042 A308950
Adjacent sequences: A234013 A234014 A234015 * A234017 A234018 A234019
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Dec 18 2013
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STATUS
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approved
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