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%I #28 Nov 13 2019 00:18:56
%S 8290,8969,9102,17998,24199,21819,20041,22084,21800,20020,21901,23792,
%T 25219,54503,55656,55767,55978,56399,55039,87290,88869,88892,88909,
%U 89108,108070,126947,141300,221901,223792,225219,554503,555656,555767,555978,556399,555039
%N Irregular table whose rows list the nontrivial cycles of the ghost iteration A329201, starting with the smallest member.
%C 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 This sequence lists these cycles, ordered by their smallest member which is always listed first.
%C Sequence A329341 gives the lengths of these cycles, i.e., rows of this table.
%C 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 The table starts:
%e n | cycle #n (length = A329341(n))
%e ---+------------------------------------------------------------------
%e 1 | 8290, 8969, 9102
%e 2 | 17998, 24199, 21819, 20041, 22084, 21800, 20020
%e 3 | 21901, 23792, 25219
%e 4 | 54503, 55656, 55767, 55978, 56399, 55039
%e 5 | 87290, 88869, 88892, 88909, 89108
%e 6 | 108070, 126947, 141300
%e 7 | 221901, 223792, 225219
%e 8 | 554503, 555656, 555767, 555978, 556399, 555039
%e 9 | 741683, 775208, 772880, 767272, 778827, 779892, 782009, 798218, 819835
%e 10 | 810001, 881002, 873900, 859210, 893921,
%e | 910592, 992139, 985013, 971501, 997952, 1000195, 900011
%e 11 | 887290, 888869, 888892, 888909, 889108
%e 12 | 1108070, 1126947, 1141300
%e 13 | 2221901, 2223792, 2225219
%e 14 | 4350630, 4476263, 4507706
%e 15 | 5461741, 5587374, 5618817
%e 16 | 5554503, 5555656, 5555767, 5555978, 5556399, 5555039
%e 17 | 6572852, 6698485, 6729928
%e 18 | 8887290, 8888869, 8888892, 8888909, 8889108
%e 19 | 9071007, 10047114, 11090717, 10890951
%e 20 | 10807007, 12694714, 14130077
%e 21 | 11108070, 11126947, 11141300
%e 22 | 22221901, 22223792, 22225219
%e 23 | 44350630, 44476263, 44507706
%e 24 | 55461741, 55587374, 55618817
%e 25 | 55554503, 55555656, 55555767, 55555978, 55556399, 55555039
%e 26 | 66572852, 66698485, 66729928
%e 27 | 88887290, 88888869, 88888892, 88888909, 88889108
%e 28 | 90710050, 100471105, 110907120, 108909508
%e 29 | 98311327, 99831542, 99679130, 99991953, 99983111,
%e | 99967911, 99936631, 99873599, 99759359, 99534735, 99113393
%e 30 | 108070010, 126947021, 141300742
%e 31 | 110807007, 112694714, 114130077
%e 32 | 111108070, 111126947, 111141300
%e 33 | 222221901, 222223792, 222225219
%e 34 | 329112807, 346914494, 359297549, 384069764, 329606552,
%e | 346972655, 334647245, 335870766, 333553056, 333755407,
%e | 334175554, 335537555, 333513355, 333271335, 333115133, 332910713, 331128951
%e 35 | 444350630, 444476263, 444507706
%e 36 | 555461741, 555587374, 555618817
%e 37 | 555554503, 555555656, 555555767, 555555978, 555556399, 555555039
%e 38 | 666572852, 666698485, 666729928
%e 39 | 829021565, 896942976, 910295697
%e 40 | 888887290, 888888869, 888888892, 888888909, 888889108
%e 41 | 998311327, 999831542, 999679130, 999991953, 999983111,
%e | 999967911, 999936631, 999873599, 999759359, 999534735, 999113393
%o (PARI)
%o 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 {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 Cf. A329341 (row lengths), A329201, A329196 (analog for A329200), A329198.
%K nonn,more,tabf
%O 1,1
%A _M. F. Hasler_, Nov 10 2019
%E Rows 12 through 41 from _Scott R. Shannon_, Nov 12 2019
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