A276083 a(0) = 0, a(2n) = A255411(a(n)), a(2n+1) = 1+A153880(a(n)).

0, 1, 4, 3, 18, 13, 16, 9, 96, 73, 76, 51, 90, 61, 64, 33, 600, 481, 484, 363, 498, 373, 376, 249, 576, 433, 436, 291, 450, 301, 304, 153, 4320, 3601, 3604, 2883, 3618, 2893, 2896, 2169, 3696, 2953, 2956, 2211, 2970, 2221, 2224, 1473, 4200, 3361, 3364, 2523, 3378, 2533, 2536, 1689, 3456, 2593, 2596, 1731, 2610, 1741, 1744, 873, 35280, 30241

Offset: 0

Author

Antti Karttunen, Aug 21 2016

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A153880, A255411.

Cf. also A059590, A275959, A276091, A225901, A276082.

Programs

Python

from sympy import factorial as f
def a007623(n, p=2): return n if n
0 else '0' for i in x)[::-1]
    return 0 if n==0 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
def a153880(n):
    x=(str(a007623(n)) + '0')[::-1]
    return 0 if n==0 else sum([int(x[i])*f(i + 1) for i in range(len(x))])
def a(n): return 0 if n==0 else a255411(a(n//2)) if n%2==0 else 1 + a153880(a((n - 1)//2))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 20 2017

Formula

a(0) = 0, a(2n) = A255411(a(n)), a(2n+1) = 1+A153880(a(n)).

Other identities. For all n >= 0:

a(n) = A225901(A276082(n)).