A276082 a(0) = 0, a(2n) = A153880(a(n)), a(2n+1) = 1+A255411(a(n)).

0, 1, 2, 5, 6, 13, 14, 23, 24, 49, 50, 77, 54, 85, 86, 119, 120, 241, 242, 365, 246, 373, 374, 503, 264, 409, 410, 557, 414, 565, 566, 719, 720, 1441, 1442, 2165, 1446, 2173, 2174, 2903, 1464, 2209, 2210, 2957, 2214, 2965, 2966, 3719, 1560, 2401, 2402, 3245, 2406, 3253, 3254, 4103, 2424, 3289, 3290, 4157, 3294, 4165, 4166, 5039, 5040, 10081

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences related to factorial base representation

Formula

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

Other identities. For all n >= 0:

a(n) = A225901(A276083(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A276082 n) (cond ((zero? n) n) ((even? n) (A153880 (A276082 (/ n 2)))) (else (+ 1 (A255411 (A276082 (/ (- n 1) 2)))))))
(Python)
from sympy import factorial as f
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a255411(n):
    x=str(a007623(n)) + '0'
    y="".join(str(int(i) + 1) if int(i)>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 a153880(a(n//2)) if n%2==0 else 1 + a255411(a((n - 1)//2))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 20 2017

Crossrefs

Cf. A153880, A255411

Cf. also A059590, A275959, A276091, A225901, A276083.

Sequence in context: A354025 A100613 A070911 * A113240 A098376 A342569

Adjacent sequences: A276079 A276080 A276081 * A276083 A276084 A276085

Keyword

nonn,base

Author

Antti Karttunen, Aug 21 2016

Status

approved