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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
1, 2, 145, 169, 1454, 40585, 363601 (list; graph; refs; listen; history; text; internal format)



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


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).


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.


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


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


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




N. J. A. Sloane, Mar 17 2019



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Last modified December 4 12:03 EST 2020. Contains 338923 sequences. (Running on oeis4.)