A389141 Least positive integer k such that A389140(k*n) has the smallest value.

1, 1, 18, 1, 1, 9, 14, 1, 6, 1, 12, 9, 2, 7, 36, 1, 2, 3, 2, 1, 6, 6, 2, 6, 1, 1, 2, 4, 2, 18, 2, 1, 4, 1, 28, 3, 4, 1, 4, 1, 4, 3, 2, 3, 12, 1, 2, 3, 2, 1, 2, 1, 4, 1, 24, 2, 2, 1, 2, 9, 2, 1, 2, 1, 4, 2, 2, 1, 2, 14, 2, 2, 2, 2, 7, 1, 2, 2, 2, 1, 2, 2, 2, 2, 4, 1, 2, 2, 2, 6

Offset

1,3

Comments

If n is not a multiple of 5, is there always some multiplier k that makes A389140(k*n) collapse to 1?

From Pontus von Brömssen, Sep 27 2025: (Start)

The minimum of A389140(k*n) is at least 15 if n is a multiple of 25 and at least 5 if n is a multiple of 5. It seems that the best of these bounds is attained for all such n, and that the minimum is 1 if n is not a multiple of 5.

It seems that a(4000) = 3 is the last term not equal to 1, 2, or 4. Moreover, it seems that

- a(n) = 1 if n > 8060, and either n == 25, 50 (mod 100) or n is even and not congruent to 10 modulo 20;

- a(n) = 2 if n > 4030, and either n is odd and not congruent to 5 (mod 10) or n == 10, 30, 70, 75, 90 (mod 100);

- a(n) = 4 if n > 2015, n == 5 (mod 10), and n is not a multiple of 25.

(End)

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Example

a(3)=18 because 3*18=54, and 54 --> 52 --> 26 --> 16 --> 8 --> 4 --> 2 --> 1.

Crossrefs

Cf. A389140.

Sequence in context: A040329 A040326 A040325 * A040324 A168623 A146774

Adjacent sequences: A389138 A389139 A389140 * A389142 A389143 A389144

Keyword

nonn,base

Author

Ali Sada, Sep 24 2025

Status

approved