login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Trajectory of 1 under repeated application of x -> A306958(x).
3

%I #20 Nov 30 2023 00:13:29

%S 1,10,11,20,91,3628810,3780821,4234421,16030,151932,3659870,6230161,

%T 303231,2261,151390,3659781,6230170,756822,2600820,1965783,6230170,

%U 756822,2600820,1965783,6230170,756822,2600820,1965783,6230170,756822,2600820

%N Trajectory of 1 under repeated application of x -> A306958(x).

%C The trajectory converges to the cycle of length 4 given in A306959.

%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 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.d.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).

%p a:= proc(n) option remember; `if`(n=1, 1, add(

%p d!*binomial(10, d), d=convert(a(n-1), base, 10)))

%p end:

%p seq(a(n), n=1..30); # _Alois P. Heinz_, Nov 28 2023

%t a[n_]:=Total[Binomial[10,#]*#!&/@IntegerDigits[n]]; NestWhileList[a,1,UnsameQ,All] (* _Ray Chandler_, Nov 30 2023 *)

%Y Cf. A306958, A306959, A306961, A306962, A306964.

%K nonn,base,easy

%O 1,2

%A _N. J. A. Sloane_, Mar 18 2019

%E a(1)=1 inserted by _Georg Fischer_, Nov 28 2023