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%I #16 May 01 2021 01:31:51
%S 0,1,2,5,6,13,14,23,24,49,50,77,54,85,86,119,120,241,242,365,246,373,
%T 374,503,264,409,410,557,414,565,566,719,720,1441,1442,2165,1446,2173,
%U 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
%N a(0) = 0, a(2n) = A153880(a(n)), a(2n+1) = 1+A255411(a(n)).
%H Antti Karttunen, <a href="/A276082/b276082.txt">Table of n, a(n) for n = 0..8191</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(0) = 0, a(2n) = A153880(a(n)), a(2n+1) = 1+A255411(a(n)).
%F Other identities. For all n >= 0:
%F a(n) = A225901(A276083(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A276082 n) (cond ((zero? n) n) ((even? n) (A153880 (A276082 (/ n 2)))) (else (+ 1 (A255411 (A276082 (/ (- n 1) 2)))))))
%o (Python)
%o from sympy import factorial as f
%o def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o def a255411(n):
%o x=str(a007623(n)) + '0'
%o y="".join(str(int(i) + 1) if int(i)>0 else '0' for i in x)[::-1]
%o return 0 if n==0 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
%o def a153880(n):
%o x=(str(a007623(n)) + '0')[::-1]
%o return 0 if n==0 else sum([int(x[i])*f(i + 1) for i in range(len(x))])
%o def a(n): return 0 if n==0 else a153880(a(n//2)) if n%2==0 else 1 + a255411(a((n - 1)//2))
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 20 2017
%Y Cf. A153880, A255411
%Y Cf. also A059590, A275959, A276091, A225901, A276083.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Aug 21 2016
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