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A329342 Irregular table whose rows list the nontrivial cycles of the ghost iteration A329201, starting with the smallest member.

%I A329342 #28 Nov 13 2019 00:18:56
%S A329342 8290,8969,9102,17998,24199,21819,20041,22084,21800,20020,21901,23792,
%T A329342 25219,54503,55656,55767,55978,56399,55039,87290,88869,88892,88909,
%U A329342 89108,108070,126947,141300,221901,223792,225219,554503,555656,555767,555978,556399,555039
%N A329342 Irregular table whose rows list the nontrivial cycles of the ghost iteration A329201, starting with the smallest member.
%C A329342 A329201 consists of adding or subtracting the number whose digits are the differences of adjacent digits of n, depending on its parity. Repdigits A010785 are fixed points of this map, but some numbers enter nontrivial cycles.
%C A329342 This sequence lists these cycles, ordered by their smallest member which is always listed first.
%C A329342 Sequence A329341 gives the lengths of these cycles, i.e., rows of this table.
%C A329342 Whenever all terms of a cycle have the same number of digits and same initial digit, then this digit can be prefixed k times to each term to obtain a different cycle of same length, for any k >= 0. (The corresponding "ghosts" A040115(n) are then the same, so the first differences are also the same and add again up to 0.) This is the case for rows 3, 4, 5, 6, ... of this table. Rows 7, 8, 11, ... are subsequent members of the respective family. We could call "primitive" the cycles which are not obtained from an earlier cycle by duplicating the initial digits.
%e A329342 The table starts:
%e A329342    n |  cycle #n  (length = A329341(n))
%e A329342   ---+------------------------------------------------------------------
%e A329342    1 |  8290,    8969,   9102
%e A329342    2 |  17998,  24199,  21819,  20041,  22084,  21800, 20020
%e A329342    3 |  21901,  23792,  25219
%e A329342    4 |  54503,  55656,  55767,  55978,  56399,  55039
%e A329342    5 |  87290,  88869,  88892,  88909,  89108
%e A329342    6 | 108070, 126947, 141300
%e A329342    7 | 221901, 223792, 225219
%e A329342    8 | 554503, 555656, 555767, 555978, 556399, 555039
%e A329342    9 | 741683, 775208, 772880, 767272, 778827, 779892, 782009, 798218, 819835
%e A329342   10 | 810001, 881002, 873900, 859210, 893921,
%e A329342      | 910592, 992139, 985013, 971501, 997952, 1000195, 900011
%e A329342   11 | 887290, 888869, 888892, 888909, 889108
%e A329342   12 | 1108070, 1126947, 1141300
%e A329342   13 | 2221901, 2223792, 2225219
%e A329342   14 | 4350630, 4476263, 4507706
%e A329342   15 | 5461741, 5587374, 5618817
%e A329342   16 | 5554503, 5555656, 5555767, 5555978, 5556399, 5555039
%e A329342   17 | 6572852, 6698485, 6729928
%e A329342   18 | 8887290, 8888869, 8888892, 8888909, 8889108
%e A329342   19 | 9071007, 10047114, 11090717, 10890951
%e A329342   20 | 10807007, 12694714, 14130077
%e A329342   21 | 11108070, 11126947, 11141300
%e A329342   22 | 22221901, 22223792, 22225219
%e A329342   23 | 44350630, 44476263, 44507706
%e A329342   24 | 55461741, 55587374, 55618817
%e A329342   25 | 55554503, 55555656, 55555767, 55555978, 55556399, 55555039
%e A329342   26 | 66572852, 66698485, 66729928
%e A329342   27 | 88887290, 88888869, 88888892, 88888909, 88889108
%e A329342   28 | 90710050, 100471105, 110907120, 108909508
%e A329342   29 | 98311327, 99831542, 99679130, 99991953, 99983111,
%e A329342      | 99967911, 99936631, 99873599, 99759359, 99534735, 99113393
%e A329342   30 | 108070010, 126947021, 141300742
%e A329342   31 | 110807007, 112694714, 114130077
%e A329342   32 | 111108070, 111126947, 111141300
%e A329342   33 | 222221901, 222223792, 222225219
%e A329342   34 | 329112807, 346914494, 359297549, 384069764, 329606552,
%e A329342      | 346972655, 334647245, 335870766, 333553056, 333755407,
%e A329342      | 334175554, 335537555, 333513355, 333271335, 333115133, 332910713, 331128951
%e A329342   35 | 444350630, 444476263, 444507706
%e A329342   36 | 555461741, 555587374, 555618817
%e A329342   37 | 555554503, 555555656, 555555767, 555555978, 555556399, 555555039
%e A329342   38 | 666572852, 666698485, 666729928
%e A329342   39 | 829021565, 896942976, 910295697
%e A329342   40 | 888887290, 888888869, 888888892, 888888909, 888889108
%e A329342   41 | 998311327, 999831542, 999679130, 999991953, 999983111,
%e A329342      | 999967911, 999936631, 999873599, 999759359, 999534735, 999113393
%o A329342 (PARI)
%o A329342 T(n,T=[n])={while(!setsearch(Set(T),n=A329201(n)), T=concat(T,n));T} \\ trajectory; a cycle if n is a member of it.
%o A329342 {U=0; M=[]; for(n=9, oo, bittest(U>>=1, 0) && next; if(M && n>M[1], print(T(M[1])); M=M[^1]); t=n; V=U; while( !bittest(U, -n+t=A329201(t)), t>n || next(2); U+=1<<(t-n)); bittest(V, t-n) || #Set(digits(t))==1 || M=setunion(M, [vecmin(T(t))]) )}
%Y A329342 Cf. A329341 (row lengths), A329201, A329196 (analog for A329200), A329198.
%K A329342 nonn,more,tabf
%O A329342 1,1
%A A329342 _M. F. Hasler_, Nov 10 2019
%E A329342 Rows 12 through 41 from _Scott R. Shannon_, Nov 12 2019