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A072410 Number of iterations of the map k -> A000001(k) needed to reach 1 starting at n, or -1 if no such number exists. 2
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 (list; graph; refs; listen; history; text; internal format)
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]

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 -> 49487365422 -> 240 -> 208 -> 51 -> 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 A072491 A051034

Adjacent sequences:  A072407 A072408 A072409 * A072411 A072412 A072413

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 03 2008

STATUS

approved

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Last modified April 19 20:37 EDT 2021. Contains 343117 sequences. (Running on oeis4.)