A283981 - OEIS

A283981

a(n) = A029931(n) - A280700(n).

0, 0, 0, 2, 0, 3, 3, 3, 0, 4, 4, 4, 4, 4, 6, 7, 0, 5, 5, 5, 5, 5, 7, 8, 5, 5, 8, 9, 8, 9, 11, 11, 0, 6, 6, 6, 6, 6, 8, 9, 6, 6, 9, 10, 9, 10, 12, 12, 6, 6, 10, 11, 10, 11, 13, 13, 10, 11, 14, 14, 14, 14, 14, 17, 0, 7, 7, 7, 7, 7, 9, 10, 7, 7, 10, 11, 10, 11, 13, 13, 7, 7, 11, 12, 11, 12, 14, 14, 11, 12, 15, 15, 15, 15, 15, 18, 7, 7, 12, 13, 12, 13, 15, 15, 12

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OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A029931(n) - A280700(n).

a(n) = A283982(n) + A124757(n).

MATHEMATICA

Table[#.Reverse@ Range@ Length@ # &@ IntegerDigits[n, 2] - DigitCount[2 n - DigitCount[2 n, 2, 1], 2, 1], {n, 0, 120}] (* Michael De Vlieger, Mar 20 2017, after Jean-François Alcover at A029931 *)

PROG

(Scheme) (define (A283981 n) (- (A029931 n) (A280700 n)))

(PARI)

a(n) = if(n<1, 0, a(n - 2^logint(n, 2)) + logint(n, 2) + 1);

b(n) = if(n<1, 0, b(n\2) + n%2);

A(n) = b(2*n - b(2*n));

for(n=0, 150, print1(a(n) - A(n), ", ")) \\ Indranil Ghosh, Mar 21 2017

(Python)

import math

def L(n): return int(math.floor(math.log(n, 2)))

def a(n): return 0 if n<1 else a(n - 2**L(n)) + L(n) + 1

def A(n): return bin(2*n - bin(2*n)[2:].count("1"))[2:].count("1")