A072410 Number of iterations of the map k -> A000001(k) needed to reach 1 starting at n, or -1 if no such number exists.

0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2

Offset: 1

Author

N. J. A. Sloane, Oct 03 2008

Keywords

• nonn

Comments

The old entry with this sequence number was a duplicate of A052409.

It appears that a(n) is the number of times n appears in A142978, excluding the first column of infinitely many 1's. - Ron Wolf, Dec 16 2020

Preceding comment is incorrect. The first counterexample is a(19) = 1, whereas 19 appears twice in A142978. - Eric M. Schmidt, Mar 22 2021

Examples

			Conway et al. remark that every number less than 2048 reaches 1 after at most 5 steps and give the following examples:
672 -> 1280 -> 1116461 -> 1
1024 -> 49487367289 -> 1
720 -> 840 -> 186 -> 6 -> 2 -> 1
320 -> 1640 -> 68 -> 5 -> 1
384 -> 20169 -> 67 -> 1
128 -> 2328 -> 64 -> 267 -> 1
960 -> 11394 -> 60 -> 13 -> 1
864 -> 4725 -> 51 -> 1
1344 -> 11720 -> 49 -> 2 -> 1
1440 -> 5958 -> 16 -> 14 -> 2 -> 1
1248 -> 1460 -> 15 -> 1
256 -> 56092 -> 11 -> 1
1728 -> 47937 -> 6 -> 2 -> 1
512 -> 10494213 -> 5 -> 1
1536 -> 408641062 -> 4 -> 2 -> 1
1664 -> 21507 -> 2 -> 1
1280 -> 1116461 -> 1
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..2047 [using data from example and A000001. a(1024) corrected by _Jinyuan Wang_, Jun 26 2022]
• John H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica.

Crossrefs

Cf. A000001, A066952 (indices of records).