

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.


5




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, 313317. MR 0472667 (57 #12362).


LINKS



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



KEYWORD

nonn,fini,full,base


AUTHOR



STATUS

approved



