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

1,2

Links

Indranil Ghosh, Table of n, a(n) for n = 1..16384

Robert G. Wilson v, Plot of first 4096 terms

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).

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}]

Prog

(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

Crossrefs

Cf. A002487, A070872-A070874.

Sequence in context: A132886 A119272 A308483 * A096115 A289838 A290734

Adjacent sequences: A070868 A070869 A070870 * A070872 A070873 A070874

Keyword

nonn

Author

N. J. A. Sloane, May 19 2002

Status

approved