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%I #8 Sep 01 2016 10:53:57
%S 0,1,2,3,1,2,3,4,5,6,4,5,2,3,4,5,3,4,1,2,3,4,2,3,4,5,6,7,5,6,7,8,9,10,
%T 8,9,6,7,8,9,7,8,5,6,7,8,6,7,3,4,5,6,4,5,6,7,8,9,7,8,5,6,7,8,6,7,4,5,
%U 6,7,5,6,2,3,4,5,3,4,5,6,7,8,6,7,4,5,6,7,5,6,3,4,5,6,4,5,1,2,3,4,2,3,4,5,6,7,5,6,3,4,5,6,4,5,2,3,4,5,3,4,5
%N a(n) = A034968(A225901(n)).
%H Antti Karttunen, <a href="/A276146/b276146.txt">Table of n, a(n) for n = 0..40320</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(n) = A034968(A225901(n)).
%t b = MixedRadix[Reverse@ Range[2, 12]]; h[n_] := Module[{s = 0, i = 2, k = n}, While[k > 0, k = Floor[n/i!]; s = s + (i - 1) k; i++]; n - s]; Table[h@ FromDigits[Map[Boole[# > 0] &, #] (Reverse@ Range[2, Length@ # + 1] - #), b] &@ IntegerDigits[n, b], {n, 0, 120}] (* Version 10.2, or *)
%t f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], Times @@ Range[# - i]]], {i, 0, #}] &@ NestWhile[# + 1 &, 0, Times @@ Range[# + 1] <= n &]; Most@ Rest[a][[All, 1]] /. {} -> {0}]; g[w_List] := Total[Times @@@ Transpose@{Map[Times @@ # &, Range@ Range[0, Length@ w]], Reverse@ Append[w, 0]}]; h[n_] := Module[{s = 0, i = 2, k = n}, While[k > 0, k = Floor[n/i!]; s = s + (i - 1) k; i++]; n - s]; Table[h@ g[Map[Boole[# > 0] &, #] (Reverse@ Range[2, Length@ # + 1] - #)] &@ f@ n, {n, 0, 120}] (* _Michael De Vlieger_, Aug 29 2016, function h after _Jean-François Alcover_ at A034968 *)
%o (Scheme) (define (A276146 n) (A034968 (A225901 n)))
%Y Cf. A034968, A225901.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Aug 29 2016
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