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%I #25 May 20 2019 14:19:20
%S 1,366784,14877,531136,29287878125,13631616,18916327,1245376,118971,1,
%T 24871,1942272,377414623,361123756,221285675921484375,453559756,
%U 16185473,4136832,113758939,366784,164961711,3179798512,131147731,1841716224,283439365914625,118754727776
%N Numbers for which the nozero power-sequence of n falls into a loop.
%C Numbers returned by the following procedure: For n = 1, 2, 3, ..., let x(n; 1) = 1. Begin the recursive sequence x(n; i) = nozero(x(n; i-1) * n), where the function nozero(x) removes all zeros from x (see A004719). When x(n; i) = x(n; j<i), return x(n; i).
%C a(10*n) = a(n). - _Pontus von Brömssen_, May 19 2019
%H Pontus von Brömssen, <a href="/A243846/b243846.txt">Table of n, a(n) for n = 1..128</a>
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a243/A243846.java">Java program</a> (github)
%F Recurrence: x(n; i) = nozero(x(n; i-1) * n), x(n; 1) = 1, i >= 2, with n >= 1. For example, for x(2;10) = 512 and nozero(512 * 2) = nozero(1024) = 124. Therefore x(2;11) = 124.
%F If the sequence {x(n; i)}_{i >= 1} becomes periodic at some entry x(n; j), that is if there exists a period length L(n) such that x(n; i + L(n)) = x(n; i) for i >= j then a(n) = x(n; j). If there is no such period length then one puts a(n) = 0.
%e a(2) = 366784 because x(2; 491) = nozero(183392 * 2) = 366784. Subsequently x(2; 527) = nozero(1533392 * 2) = nozero(3066784) = 366784, and this happens for the first time. Therefore x(2; 527) = x(2; 491) and the procedure returns x(2; 527) = 366784.
%e a(3) = 14877 because x(3; 28) = nozero(469359 * 3) = nozero(1408077) = 14877. Subsequently, x(3; 108) = nozero(4959 * 3) = 14877, and this happens for the first time. Therefore x(3; 28) = x(3; 108) and the procedure returns x(3;108) = 14877.
%t a[n_] := Block[{h = <||>, t = n}, While[! KeyExistsQ[h,t], h[t]=0; t = FromDigits@ Select[ IntegerDigits[n t], # > 0 &]]; t]; Array[a, 20] (* _Giovanni Resta_, May 20 2019 *)
%Y Cf. A004719, A242350, A243845, A306569.
%K nonn,base
%O 1,2
%A _Anthony Sand_, Jun 12 2014
%E Edited: Comment, formula and example reformulated. - _Wolfdieter Lang_, Jul 13 2014
%E a(5), a(6), a(8), a(9) corrected by _Pontus von Brömssen_, May 19 2019
%E a(10)-a(26) from _Giovanni Resta_, May 20 2019
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