A306955 Let f map k to the sum of the factorials of the digits of k (A061602); sequence lists numbers such that f(f(f(k)))=k.

1, 2, 145, 169, 1454, 40585, 363601

Offset: 1

Author

N. J. A. Sloane, Mar 17 2019

Keywords

• nonn
• fini
• full
• base

Comments

Kiss showed that there are no further terms and in fact there are no further cycles other than those shown in A014080 and A254499.

Examples

			The map f sends 169 to 363601 to 1454 to 169 ...
		

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

• P. Kiss, A generalization of a problem in number theory, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.
• G. D. Poole, Integers and the sum of the factorials of their digits, Math. Mag., 44 (1971), 278-279, [JSTOR].
• H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example I.1.b.

Crossrefs

Cf. A061602.

The fixed points and loops of length 2 can be found in A014080, A214285, and A254499.

Programs

Mathematica

f[k_] := Total[IntegerDigits[k]!]; Select[Range[400000], Nest[f, #, 3] == # &] (* Amiram Eldar, Mar 17 2019 *)

PARI

a061602(n) = my(d=digits(n)); sum(i=1, #d, d[i]!)
is(n) = a061602(a061602(a061602(n)))==n \\ Felix Fröhlich, May 18 2019