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

1,4

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

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.

Example

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

Crossrefs

Cf. A000001, A066952 (indices of records).

Sequence in context: A052299 A071854 A183025 * A342824 A344713 A072491

Adjacent sequences: A072407 A072408 A072409 * A072411 A072412 A072413

Keyword

nonn

Author

N. J. A. Sloane, Oct 03 2008

Status

approved