A362626 a(n) is the smallest number of 1's used in expressing n as a calculation containing only decimal repunits and operators +, -, * and /, where fractions are allowed as intermediate results.

1, 2, 3, 4, 5, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 7, 6, 6, 5, 5, 4, 5, 5, 6, 6, 7, 7, 7, 6, 7, 6, 5, 6, 7, 6, 6, 7, 7, 7, 8, 7, 7, 6, 7, 7, 8, 7, 8, 7, 8, 8, 8, 7, 6, 6, 7, 8, 8, 7, 7, 8, 8, 8, 8, 7, 8, 8, 8, 9, 9, 8, 8, 7, 8, 9, 8, 8, 9, 8, 8, 9, 10, 9, 9, 9, 8, 7, 7

Offset: 1

Author

Yifan Xie, Haochen Mi and Michael S. Branicky, Apr 28 2023

Keywords

• nonn
• base

Comments

a(n+1) <= a(n) + 1.

a(n) <= a(i) + a(j), for all i O j = n, for O = +, -, *, /.

Examples

			a(74) = 7, since 74 = 111/(1+(1/(1+1))).
a(111) = 3.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002275, A005245, A362471.