A284013 a(n) = n - A002487(n).

0, 0, 1, 1, 3, 2, 4, 4, 7, 5, 7, 6, 10, 8, 11, 11, 15, 12, 14, 12, 17, 13, 17, 16, 22, 18, 21, 19, 25, 22, 26, 26, 31, 27, 29, 26, 32, 26, 31, 29, 37, 30, 34, 30, 39, 33, 39, 38, 46, 40, 43, 39, 47, 40, 46, 44, 53, 47, 51, 48, 56, 52, 57, 57, 63, 58, 60, 56, 63, 55, 61, 58, 68, 58, 63, 57, 69, 60, 68, 66, 77, 67, 71, 64, 76, 64

Offset: 0

Author

Antti Karttunen, Mar 23 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A002487, A265397, A283474, A284007.

Programs

Mathematica

a[n_] :=If[n<2, n, If[ EvenQ[n], a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]]; Table[n - a[n], {n , 0, 100}] (* Indranil Ghosh, Mar 23 2017 *)

PARI

A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
for(n=0, 151, print1(n - A(n),", ")) \\ Indranil Ghosh, Mar 23 2017

Python

def a(n): return n if n<2 else (a(n//2) if n%2==0 else a((n - 1)//2) + a((n + 1)//2))
print([n - a(n) for n in range(101)]) # Indranil Ghosh, Mar 23 2017

Python

from functools import reduce
def A284013(n): return n-sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(n)[-1:2:-1],(1,0))) if n else 0 # Chai Wah Wu, May 18 2023

Scheme

(define (A284013 n) (- n (A002487 n))) ;; Code for A002487 given under that entry.

Formula

a(n) = n - A002487(n).