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

Offset: 1

Author

Jaeyool Park, Jul 10 2012

Keywords

• nonn
• base
• tabf
• fini
• full

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

Examples

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

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.
• 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.

Crossrefs

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