A306958 If the decimal expansion of n is d_1 ... d_k, a(n) = Sum d_i!*binomial(10,d_i).

1, 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800, 11, 20, 100, 730, 5050, 30250, 151210, 604810, 1814410, 3628810, 91, 100, 180, 810, 5130, 30330, 151290, 604890, 1814490, 3628890, 721, 730, 810, 1440, 5760, 30960, 151920, 605520

Offset

0,2

Comments

Kiss found all the finite cycles under iteration of this map. There is one each of lengths 2, 4, 26, and 39. See A306959-A306962.

References

P. Kiss, A generalization of a problem in number theory, Math. Sem. Notes Kobe Univ., 5 (1977), no. 3, 313-317. MR 0472667 (57 #12362).

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

P. Kiss, A generalization of a problem in number theory, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.

H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example I.1.d.

Example

The map f sends 12 to 100 to 12. This is the unique cycle of length 2.

Mathematica

a[n_] := Total[Binomial[10, #]*#! & /@ IntegerDigits[n]]; Array[a, 40, 0] (* Amiram Eldar, Mar 18 2019 *)

Crossrefs

Cf. A306957.

For trajectory of k under repeated application of f, see: A306959 and A306960 (k=1), A306964 (k=2), A306961 (k=3), A306962 (k=4).

Sequence in context: A202576 A201723 A228418 * A306957 A319893 A319874

Adjacent sequences: A306955 A306956 A306957 * A306959 A306960 A306961

Keyword

nonn,look,base

Author

N. J. A. Sloane, Mar 18 2019

Status

approved