A047988 - OEIS

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A047988

Start with n and reach 2 by repeatedly either dividing by d where d <= the square root or by adding or subtracting 1. The division steps are free, but adding or subtracting 1 costs 1 point. a(n) is the smallest cost to reach 2.

0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,18

LINKS

David A. Corneth, Table of n, a(n) for n = 2..10001

David A. Corneth, PARI program

Thomas Kantke, Das Spiel Minimum und die Zerlegung natürlicher Zahlen, Mathematische Unterhaltungen, Spectrum der Wissenschaft, April 1993, pp. 11-13.

EXAMPLE

From David A. Corneth, Jun 05 2020: (Start)

For n = 19 we get to 2 via

n := 19 - 1 = 2 (+1 point as we subtract 1 from n)

n := 18/3 = 6 (+0 point as we divide by a divisor)

n := 6/2 = 3 (+0 point, we divide by a divisor. we can't divide by 3 as 3 > sqrt(6)).

n := 3 - 1 = 2 (+1 point; steps end here; we have n = 2)

We earned 2 points in these steps. As this is the minimal number of points starting at n = 19, a(19) = 2. (End)

PROG

(PARI) \\ see Corneth link \\ David A. Corneth, Jun 05 2020

CROSSREFS

Cf. A047836, A047984, A047985, A047986, A047987.