

A214285


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


6




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, 313317. 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. 12, 1974), 145149.
Jaeyool Park, Blog [in Korean].
G. D. Poole, Integers and the sum of the factorials of their digits, Math. Mag., 44 (1971), 278279, [JSTOR].
Project Euler, Problem 74Digit factorial chains
H. J. J. te Riele, Iteration of numbertheoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345360. See Example I.1.b.


EXAMPLE

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


MAPLE

with(numtheory);
A214285:=proc(q)
local a, b, c, d, i, n;
for n from 1 to q do
a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; c:=0; d:=0;
for i from 1 to b do c:=c+(atrunc(a/10)*10)!; a:=trunc(a/10); od;
a:=c; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=c;
for i from 1 to b do d:=d+(atrunc(a/10)*10)!; a:=trunc(a/10); od;
if n=d and n<>c then lprint(n, c); fi;
od; end:
A214285(1000000000000) # Paolo P. Lava, Jul 10 2012


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



