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%I #14 Nov 26 2015 00:18:28
%S 1,2,12,22,122,3,13,23,123,223,1223,33,133,233,1233,2233,12233,333,
%T 1333,2333,12333,22333,122333,4,14,24,124,224,1224,34,134,234,1234,
%U 2234,12234,334,1334,2334,12334,22334
%N n = Sum_{b} c_b*b! in the factorial base rewritten by c_b-fold repetition of b, b=1,2,3,....
%C The integer n has a unique "greedy" representation in the factorial base as n = Sum_{b>=1} c_b*b!, see A007623.
%C The number of coefficients c_b is A084558(n).
%C The current sequence starts from an empty string, scans the coefficients c_b in the order b=1,2,3,..., i.e., reads A007623(n) from the least to the most significant position, and appends b c_b times to the string. The resulting string is shown in the sequence as a standard decimal number a(n).
%F A061602(a(n)) = n. - _R. J. Mathar_, Oct 30 2010
%e a(39) = 12334 with A007623(39) = 1211, because 1! + 2! + 3! + 3! + 4! = 1 + 2 + 6 + 6 + 24 = 39
%Y Cf. A005096, A007623, A108911.
%K nonn,base
%O 1,2
%A _Giorgio Balzarotti_ and _Paolo P. Lava_, Oct 13 2005
%E Definition and comment shortened with reference to A007623 - _R. J. Mathar_, Oct 30 2010
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