# [seqfan] Re: Recurring Digital Invariant

Hans Havermann pxp at rogers.com
Wed Feb 18 01:59:36 CET 2009

```Eric Angelini:

> ... what if k = "length of the considered integer"?

If I am doing this correctly, here are the first 34 cycles (by size of
smallest precursor). The format for each is index, {smallest
precursor, cycle length, {the cycle itself with the smallest element
of the cycle first}}:

1 {1, 1, {1}}
2 {2, 1, {2}}
3 {3, 1, {3}}
4 {4, 1, {4}}
5 {5, 1, {5}}
6 {6, 1, {6}}
7 {7, 1, {7}}
8 {8, 1, {8}}
9 {9, 1, {9}}
10 {14, 1, {370}}
11 {59, 3, {160, 217, 352}}
12 {108, 1, {153}}
13 {119, 1, {371}}
14 {136, 2, {136, 244}}
15 {138, 10, {259, 862, 736, 586, 853, 664, 496, 1009, 6562, 3233}}
16 {147, 14, {18829, 124618, 312962, 578955, 958109, 1340652, 376761,
329340, 537059, 681069, 886898, 1626673, 1665667, 2021413}}
17 {177, 2, {58618, 76438}}
18 {389, 6, {2929, 13154, 4394, 7154, 3283, 4274}}
19 {407, 1, {407}}
20 {559, 3, {282595, 824963, 845130}}
21 {709, 1, {8208}}
22 {999, 2, {2178, 6514}}
23 {1118, 4, {10933, 59536, 73318, 50062}}
24 {1157, 12, {5908997, 17347727, 23131558, 17571846, 30442597,
49340036, 44870531, 23070276, 13216291, 44733413, 5981093, 11743403}}
25 {1346, 1, {1634}}
26 {4479, 1, {9474}}
27 {11227, 1, {54748}}
28 {12399, 1, {32164049651}}
29 {22779, 1, {92727}}
30 {30489, 1, {93084}}
31 {100666, 12, {1680387, 5299971, 15250704, 6611844, 2689794,
12783081, 39326052, 45130596, 45579685, 68505765, 27073124, 11602212}}
32 {127779, 1, {548834}}
33 {577999, 1, {4210818}}
34 {677779, 3, {2767918,8807272,5841646}}

```