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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

Table of n, a(n) for n=1..36.

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.)