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%I #42 Mar 05 2024 11:28:21
%S 871,45361,872,45362
%N 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.
%C 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.
%C Peter Kiss (1977) showed there are no further terms. - _N. J. A. Sloane_, Mar 17 2019
%D 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).
%H P. Kiss, <a href="http://real-j.mtak.hu/9373/1/MTA_MatematikaiLapok_1974.pdf">A generalization of a problem in number theory</a>, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.
%H Jaeyool Park, <a href="http://numberer.blogspot.kr/2012/07/factorions.html">Blog</a> [in Korean].
%H G. D. Poole, <a href="https://doi.org/10.1080/0025570X.1971.11976172">Integers and the sum of the factorials of their digits</a>, Math. Mag., 44 (1971), 278-279, <a href="https://www.jstor.org/stable/2688641">[JSTOR]</a>.
%H Project Euler, <a href="http://projecteuler.net/problem=74">Problem 74-Digit factorial chains</a>
%H Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke Minematsu, Kou Omori, and Ryohei Miyadera, <a href="https://arxiv.org/abs/2308.06691">Curious Properties of Iterative Sequences</a>, arXiv:2308.06691 [math.GM], 2023.
%H H. J. J. te Riele, <a href="https://ir.cwi.nl/pub/6662">Iteration of number-theoretic functions</a>, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example I.1.b.
%e 8! + 7! + 1! = 45361, 4! + 5! + 3! + 6! + 1! = 871.
%Y Cf. A061602, A014080, A188284, A254499, A306955.
%K nonn,base,tabf,fini,full
%O 1,1
%A _Jaeyool Park_, Jul 10 2012
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