

A111095


n = Sum_{b} c_b*b! in the factorial base rewritten by c_bfold repetition of b, b=1,2,3,....


3



1, 2, 12, 22, 122, 3, 13, 23, 123, 223, 1223, 33, 133, 233, 1233, 2233, 12233, 333, 1333, 2333, 12333, 22333, 122333, 4, 14, 24, 124, 224, 1224, 34, 134, 234, 1234, 2234, 12234, 334, 1334, 2334, 12334, 22334
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The integer n has a unique "greedy" representation in the factorial base as n = Sum_{b>=1} c_b*b!, see A007623.
The number of coefficients c_b is A084558(n).
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).


LINKS

Table of n, a(n) for n=1..40.


FORMULA

A061602(a(n)) = n.  R. J. Mathar, Oct 30 2010


EXAMPLE

a(39) = 12334 with A007623(39) = 1211, because 1! + 2! + 3! + 3! + 4! = 1 + 2 + 6 + 6 + 24 = 39


CROSSREFS

Cf. A005096, A007623, A108911.
Sequence in context: A120672 A190642 A108960 * A073211 A233137 A094626
Adjacent sequences: A111092 A111093 A111094 * A111096 A111097 A111098


KEYWORD

nonn,base


AUTHOR

Giorgio Balzarotti and Paolo P. Lava, Oct 13 2005


EXTENSIONS

Definition and comment shortened with reference to A007623  R. J. Mathar, Oct 30 2010


STATUS

approved



