A214285 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A214285

List of amicable sums-of-factorial-of-digits pairs (A,B): A equals the sum of the factorials of B's digits in base 10, and vice versa.

871, 45361, 872, 45362

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Number pairs (A,B), A <> B, such that A061602(A)=B and A061602(B)=A, indicating where the mapping of A to the sum of the factorials of its digits has a cycle of length 2.

Peter Kiss (1977) showed there are no further terms. - N. J. A. Sloane, Mar 17 2019

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..4.

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

Jaeyool Park, Blog [in Korean].

G. D. Poole, Integers and the sum of the factorials of their digits, Math. Mag., 44 (1971), 278-279, [JSTOR].

Project Euler, Problem 74-Digit factorial chains

Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke Minematsu, Kou Omori, and Ryohei Miyadera, Curious Properties of Iterative Sequences, arXiv:2308.06691 [math.GM], 2023.

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

8! + 7! + 1! = 45361, 4! + 5! + 3! + 6! + 1! = 871.

CROSSREFS

Cf. A061602, A014080, A188284, A254499, A306955.

Sequence in context: A317806 A031783 A253167 * A251841 A251085 A334011

Adjacent sequences: A214282 A214283 A214284 * A214286 A214287 A214288

KEYWORD

nonn,base,tabf,fini,full

AUTHOR

Jaeyool Park, Jul 10 2012

STATUS

approved