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A328865 The first repeating term in the trajectory of n under iterations of A329623, or -1 if no such terms exists.

%I A328865 #96 Jul 16 2020 11:47:52
%S A328865 1,2,3,4,5,6,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%T A328865 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U A328865 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A328865 The first repeating term in the trajectory of n under iterations of A329623, or -1 if no such terms exists.
%C A328865 A329623(n) = |n - A053392(n)|, where A053392 is the concatenation of the sums of pairs of consecutive digits.
%C A328865 This is the first number which appears twice for the iteration of A329623 starting with n. See A329624 for an explanation of the sequence, and for the number of iterations required before reaching this value. Terms a(9) to a(127) are all 9's, after which the sequence shows large jumps in value, e.g., a(1673) = 62626262626262626262626262637.
%C A328865 All -1 are so far conjectural, see A329624 and A329917 for more information.
%C A328865 The terms > 0 of this sequence are elements of cycles for A329623. Only 2-cycles and fixed points 1, 2, ..., 9 and 4...455 are known. Therefore a(n) is the earliest A329623^{k}(n) = A329623^{k+2}(n) if such k exist. See A328142 for the list of all possible values and more precise definitions. - _M. F. Hasler_, Dec 06 2019
%C A328865 The first escape value is a(1373) = -1. - _Georg Fischer_, Jul 16 2020
%H A328865 Scott R. Shannon, <a href="/A328865/b328865.txt">Table of n, a(n) for n = 1..10000</a>
%e A328865 a(10) = 9 as A329623(10) = 9, and A329623(9) = 9, thus 9 is the first repeating value.
%e A328865 a(128) = 182, as A329623(128) = 182, A329623(182) = 728, A329623(728) = 182, thus 182 is the first repeating value.
%e A328865 a(210) = 637, as A329623(210) = 179, A329623(179) = 637, A329623(637) = 273, A329623(273) = 637, thus 637 is the first repeating value.
%o A328865 (PARI) A328865(n,L=n^10)={my(o);-!until(n>L,o==(n=A329623(o=n))&&return(n))} \\ _M. F. Hasler_, Dec 06 2019
%Y A328865 Cf. A329623, A329624, A329917, A329200, A329197.
%K A328865 sign,base
%O A328865 1,2
%A A328865 _Scott R. Shannon_, Nov 24 2019
%E A328865 Incorrect comment, link and program deleted following an observation by _Scott R. Shannon_, Nov 27 2019