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.
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
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