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A084318 Iterate function described in A084317 if started at initial value n until reaching a fixed point.

%I A084318 #11 Oct 15 2013 22:32:02
%S A084318 0,2,3,2,5,23,7,2,3,5,11,23,13,3,1129,2,17,23,19,5,37,211,23,23,5,
%T A084318 3251,3,3,29,547,31,2,311,31397,1129,23,37,373,313,5,41,379,43,211,
%U A084318 1129,223,47,23,7,5,317,3251,53,23,773,3,1129,229,59,547,61,31237,37,2,1129,2311
%N A084318 Iterate function described in A084317 if started at initial value n until reaching a fixed point.
%C A084318 Conjecture: fixed point always exists.
%C A084318 Some initial values capriciously provide very large prime fixed-points. This behavior is illustrated in A084319 for initial value n=91.
%C A084318 Unlike the related home primes A037274, the trajectory of numbers in this procedure is not strictly increasing. Of the 8770 numbers < 10000 that have trajectories (that is, that are neither 1 nor prime) 3727 decrease at least once before reaching 30 digits. A sequence with no decreases is twice as likely to not terminate before 30 digits (10.0%) as one that has at least one decrease (4.8%). - _Christian N. K. Anderson_, May 04 2013
%H A084318 Christian N. K. Anderson, <a href="/A084318/a084318_1.txt">Table of n, steps to reach a(n), and a(n)</a> for numbers where a(n) has fewer than 30 digits; NA otherwise. Also includes trajectories, factors separated by |s.
%e A084318 a(0)=0 since no prime factors to concatenate;
%e A084318 a[p^j]=p for p prime(powers);
%e A084318 n=95=519: fixed-point list is {95,519,3173,19167,36389},
%e A084318 so a(95)=36389, a prime.
%t A084318 ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] conc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[FixedPoint[conc, w], {w, 1, 90}] Table[conc[w], {w, 1, 128}]
%Y A084318 Cf. A084317, A084319.
%K A084318 base,nonn
%O A084318 1,2
%A A084318 _Labos Elemer_, Jun 16 2003