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

1,2

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.

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

Table of n, a(n) for n=1..7.

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A061602.

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

Sequence in context: A093002 A074319 A188284 * A228507 A254499 A071064

Adjacent sequences: A306952 A306953 A306954 * A306956 A306957 A306958

Keyword

nonn,fini,full,base

Author

N. J. A. Sloane, Mar 17 2019

Status

approved