A111095 n = Sum_{b} c_b*b! in the factorial base rewritten by c_b-fold repetition of b, b=1,2,3,....

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

Offset: 1

Author

Giorgio Balzarotti and Paolo P. Lava, Oct 13 2005

Keywords

• nonn
• base

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).

Examples

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

Crossrefs

Cf. A005096, A007623, A108911.

Formula

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

Extensions

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