A188284 -id:A188284 - cp's OEIS frontend

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

Jaeyool Park, Jul 10 2012

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

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

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).

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.

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

A188283 Numbers k such that iterations for the map r -> A061602(r) starting with k ends with a fixed point (factorions A014080).

Original entry on oeis.org

0, 1, 2, 10, 11, 145, 154, 223, 232, 322, 405, 415, 450, 451, 504, 514, 540, 541, 569, 596, 659, 695, 956, 965, 1023, 1032, 1123, 1132, 1203, 1213, 1223, 1230, 1231, 1232, 1302, 1312, 1320, 1321, 1322, 1449, 1494, 1569, 1596, 1659, 1695, 1944, 1956, 1965, 2003

Offset: 1

Jaroslav Krizek, Mar 26 2011

If k is a term, then (10^k - 1)/9 is also a term. - Jinyuan Wang, Nov 07 2020

			Number 405 is in sequence because 405 -> 145 -> 145 -> ...

Supersequence of A014080 (factorions).

Cf. A061602, A173447, A188284.

is(k) = {my(t=k, v=List([k])); while(t=sum(i=1, #d=digits(t), d[i]!), if(t==v[#v], return(1), if(sum(i=1, #v-1, t==v[i]), return(0))); listput(v, t)); } \\ Jinyuan Wang, Nov 07 2020

Missing terms a(1) and a(8)-a(10) added by Jaroslav Krizek, Jan 28 2012

Name corrected and more terms from Jinyuan Wang, Nov 07 2020

cp's OEIS Frontend

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.

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