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 A329342 Irregular table whose rows list the nontrivial cycles of the ghost iteration A329201, starting with the smallest member. 5
 8290, 8969, 9102, 17998, 24199, 21819, 20041, 22084, 21800, 20020, 21901, 23792, 25219, 54503, 55656, 55767, 55978, 56399, 55039, 87290, 88869, 88892, 88909, 89108, 108070, 126947, 141300, 221901, 223792, 225219, 554503, 555656, 555767, 555978, 556399, 555039 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. This sequence lists these cycles, ordered by their smallest member which is always listed first. Sequence A329341 gives the lengths of these cycles, i.e., rows of this table. 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. LINKS EXAMPLE The table starts: n | cycle #n (length = A329341(n)) ---+------------------------------------------------------------------ 1 | 8290, 8969, 9102 2 | 17998, 24199, 21819, 20041, 22084, 21800, 20020 3 | 21901, 23792, 25219 4 | 54503, 55656, 55767, 55978, 56399, 55039 5 | 87290, 88869, 88892, 88909, 89108 6 | 108070, 126947, 141300 7 | 221901, 223792, 225219 8 | 554503, 555656, 555767, 555978, 556399, 555039 9 | 741683, 775208, 772880, 767272, 778827, 779892, 782009, 798218, 819835 10 | 810001, 881002, 873900, 859210, 893921, | 910592, 992139, 985013, 971501, 997952, 1000195, 900011 11 | 887290, 888869, 888892, 888909, 889108 12 | 1108070, 1126947, 1141300 13 | 2221901, 2223792, 2225219 14 | 4350630, 4476263, 4507706 15 | 5461741, 5587374, 5618817 16 | 5554503, 5555656, 5555767, 5555978, 5556399, 5555039 17 | 6572852, 6698485, 6729928 18 | 8887290, 8888869, 8888892, 8888909, 8889108 19 | 9071007, 10047114, 11090717, 10890951 20 | 10807007, 12694714, 14130077 21 | 11108070, 11126947, 11141300 22 | 22221901, 22223792, 22225219 23 | 44350630, 44476263, 44507706 24 | 55461741, 55587374, 55618817 25 | 55554503, 55555656, 55555767, 55555978, 55556399, 55555039 26 | 66572852, 66698485, 66729928 27 | 88887290, 88888869, 88888892, 88888909, 88889108 28 | 90710050, 100471105, 110907120, 108909508 29 | 98311327, 99831542, 99679130, 99991953, 99983111, | 99967911, 99936631, 99873599, 99759359, 99534735, 99113393 30 | 108070010, 126947021, 141300742 31 | 110807007, 112694714, 114130077 32 | 111108070, 111126947, 111141300 33 | 222221901, 222223792, 222225219 34 | 329112807, 346914494, 359297549, 384069764, 329606552, | 346972655, 334647245, 335870766, 333553056, 333755407, | 334175554, 335537555, 333513355, 333271335, 333115133, 332910713, 331128951 35 | 444350630, 444476263, 444507706 36 | 555461741, 555587374, 555618817 37 | 555554503, 555555656, 555555767, 555555978, 555556399, 555555039 38 | 666572852, 666698485, 666729928 39 | 829021565, 896942976, 910295697 40 | 888887290, 888888869, 888888892, 888888909, 888889108 41 | 998311327, 999831542, 999679130, 999991953, 999983111, | 999967911, 999936631, 999873599, 999759359, 999534735, 999113393 PROG (PARI) 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. {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))]) )} CROSSREFS Cf. A329341 (row lengths), A329201, A329196 (analog for A329200), A329198. Sequence in context: A031589 A031769 A280872 * A237948 A250991 A206192 Adjacent sequences: A329339 A329340 A329341 * A329343 A329344 A329345 KEYWORD nonn,more,tabf AUTHOR M. F. Hasler, Nov 10 2019 EXTENSIONS Rows 12 through 41 from Scott R. Shannon, Nov 12 2019 STATUS approved

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Last modified January 28 15:37 EST 2023. Contains 359895 sequences. (Running on oeis4.)