A118522 Define sequence S_n by: initial term = n, reverse digits and add 3 to get next term. It is conjectured that S_n always reaches a cycle. Sequence gives number of steps for S_n to reach a cycle.

1, 3, 3, 0, 2, 2, 0, 1, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 3, 0, 0, 14, 0, 0, 0, 4, 0, 0, 3, 0, 0, 11, 5, 13, 10, 3, 6, 6, 1, 5, 5, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 7, 0, 0, 12, 0, 0, 0, 2, 0, 0, 7, 0, 0, 9, 3, 11, 8, 1, 4, 4, 2, 3, 3, 2, 0, 0, 2, 0, 0, 0, 6, 0, 0, 5, 0, 0, 10, 0, 0, 0, 6, 0, 0

Offset: 1

Author

N. J. A. Sloane, May 06 2006

Keywords

• nonn
• base

Comments

Initial cycles have length 3 or 6.

From Lars Blomberg, Jan 15 2018: (Start)

For n < 10^8, the only cycles found are the following:

[4,7,10]

[18,84,51]

[29,95,62]

[11,14,44,47,77,80]

[12,24,45,57,78,90]

[15,54,48,87,81,21]

[16,64,49,97,82,31]

[19,94,52,28,85,61]

[22,25,55,58,88,91]

[26,65,59,98,92,32]

The union of all of them has 51 terms (= 3*3 + 7*6): [4, 7, 10, 11, 12, 14, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 44, 45, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 61, 62, 64, 65, 77, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 94, 95, 97, 98] (End)

Links

• Lars Blomberg, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Crossrefs

For records see A118523, A118524. Cf. A117831. For S_1, S_2 etc. see A118517-A118521.