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%I A322001 #8 Dec 01 2018 08:57:10
%S A322001 0,1,2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,10,11,4,5,6,7,8,9,10,11,12,13,6,
%T A322001 7,8,9,10,11,12,13,14,15,8,9,10,11,12,13,14,15,16,17,10,11,12,13,14,
%U A322001 15,16,17,18,19,12,13,14,15,16,17,18,19,20,21,14,15,16,17,18,19,20,21,22,23,16,17,18,19,20,21,22,23,24,25,18,19,20,21,22,23,24,25,26,27,6
%N A322001 Digits of n interpreted in factorial base: a(Sum d_k*10^k) = Sum d_k*k!
%C A322001 More terms than usual are given to distinguish the sequence from A081594, A028897 and A244158, which agree up to a(99). The last two correspond to k! replaced by 2^k resp. Catalan(k).
%C A322001 This is a left inverse to A007623 (factorial base representation of n): A322001(A007623(n)) = n for all n >= 0. One could imagine variants which have a(n) = 0 or a(n) = -1 if n is not a term of A007623. Restricted to the range of A007623, it is also a right inverse to A007623, at least up to the 10 digit terms, beyond which A007623 becomes non-injective.
%t A322001 a[n_] := Module[{d=Reverse@IntegerDigits[n]}, Sum[d[[i]]*i!, {i,1,Length[d]}]]; Array[a, 100, 0] (* _Amiram Eldar_, Nov 28 2018 *)
%o A322001 (PARI) A322001(n)=sum(i=1,#n=Vecrev(digits(n)),n[i]*i!) \\ _M. F. Hasler_, Nov 27 2018
%Y A322001 Cf. A007623 (right inverse), A081594, A028897, A244158.
%K A322001 nonn,base
%O A322001 0,3
%A A322001 _M. F. Hasler_, Nov 27 2018

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