A070871 a(n) = A002487(n) * A002487(n+1) (Conway's alimentary function).

1, 2, 2, 3, 6, 6, 3, 4, 12, 15, 10, 10, 15, 12, 4, 5, 20, 28, 21, 24, 40, 35, 14, 14, 35, 40, 24, 21, 28, 20, 5, 6, 30, 45, 36, 44, 77, 70, 30, 33, 88, 104, 65, 60, 84, 63, 18, 18, 63, 84, 60, 65, 104, 88, 33, 30, 70, 77, 44, 36, 45, 30, 6, 7, 42, 66

Offset: 1

Author

N. J. A. Sloane, May 19 2002

Keywords

• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..16384
• Robert G. Wilson v, Plot of first 4096 terms

Crossrefs

Cf. A002487, A070872-A070874.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, n,
     (q-> b(q)+(n-2*q)*b(n-q))(iquo(n, 2)))
    end:
a:= n-> b(n)*b(n+1):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 11 2021

Mathematica

a[0] = 1; a[n_] := If[ OddQ[n], a[n/2 - 1/2], a[n/2] + a[n/2 - 1]]; Table[ a[n - 1]*a[n], {n, 1, 70}]

Python

def a002487(n): return n if n<2 else a002487(n/2) if n%2==0 else a002487((n - 1)/2) + a002487((n + 1)/2)
def a(n): return a002487(n)*a002487(n + 1) # Indranil Ghosh, Jun 08 2017

Python

from functools import reduce
def A070871(n): return 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)))*sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(n+1)[-1:2:-1],(1,0))) # Chai Wah Wu, May 05 2023

Formula

Sum of reciprocals of k-th "chunk" (between two entries k) = 1 (for example for the third chunk, 1/3 + 1/6 + 1/6 + 1/3 = 1).