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A275959 Sum of distinct terms of A002674: a(0) = 0, a(2n) = A255411(A153880(a(n))), a(2n+1) = 1+A255411(A153880(a(n))).

%I A275959 #27 May 21 2021 10:05:57
%S A275959 0,1,12,13,360,361,372,373,20160,20161,20172,20173,20520,20521,20532,
%T A275959 20533,1814400,1814401,1814412,1814413,1814760,1814761,1814772,
%U A275959 1814773,1834560,1834561,1834572,1834573,1834920,1834921,1834932,1834933,239500800,239500801,239500812,239500813,239501160,239501161,239501172,239501173,239520960,239520961
%N A275959 Sum of distinct terms of A002674: a(0) = 0, a(2n) = A255411(A153880(a(n))), a(2n+1) = 1+A255411(A153880(a(n))).
%C A275959 Fixed points of involution A225901.
%C A275959 This can be also viewed as a function that reinterprets base-2 representation of n in base-((2n)!/2) where the digits are multiplied with the successive terms of A002674, thus a(0) = 0.
%H A275959 Antti Karttunen, <a href="/A275959/b275959.txt">Table of n, a(n) for n = 0..8191</a>
%H A275959 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A275959 a(0) = 0, a(2n) = A255411(A153880(a(n))), a(2n+1) = 1+A255411(A153880(a(n))).
%F A275959 a(n) = A276089(A276091(n)).
%o A275959 (Scheme, three versions. Some require _Antti Karttunen_'s IntSeq-library)
%o A275959 ;; This implements the given recurrence:
%o A275959 (definec (A275959 n) (cond ((zero? n) n) ((even? n) (A255411 (A153880 (A275959 (/ n 2))))) (else (+ 1 (A255411 (A153880 (A275959 (/ (- n 1) 2))))))))
%o A275959 (define (A275959 n) (A276089 (A276091 n)))
%o A275959 (define A275959 (FIXED-POINTS 0 0 A225901)) ;; Slow!
%o A275959 (Python)
%o A275959 from sympy import factorial as f
%o A275959 def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o A275959 def a255411(n):
%o A275959     x=(str(a007623(n)) + '0')
%o A275959     y="".join(str(int(i) + 1) if int(i)>0 else '0' for i in x)[::-1]
%o A275959     return 0 if n==0 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
%o A275959 def a153880(n):
%o A275959     x=(str(a007623(n)) + '0')[::-1]
%o A275959     return 0 if n==0 else sum([int(x[i])*f(i + 1) for i in range(len(x))])
%o A275959 def a(n): return 0 if n==0 else a255411(a153880(a(n//2))) if n%2==0 else 1 + a255411(a153880(a((n - 1)//2)))
%o A275959 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 20 2017
%Y A275959 Cf. A002674, A059590, A153880, A255411, A276082, A276083, A276091.
%Y A275959 Fixed points of A225901.
%Y A275959 Subsequence of A275956 and of A276089.
%K A275959 nonn,base
%O A275959 0,3
%A A275959 _Antti Karttunen_, Aug 16 2016