A362471 a(n) is the smallest number of 1's used in expressing n as a calculation containing only decimal repunits and operators +, -, * and /.

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, 9, 8, 9, 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 21 2023

Keywords

• nonn
• base

Comments

Here, fractions are not allowed as intermediate results.

See A362626 for the variant that allows such fractions. The sequences differ first at a(74) and its immediate neighbors, since a(74) = 8 > 7 = A362626(74). See the example in A362626. - Peter Munn, Apr 28 2023

Examples

			For n = 6, 6 = (1+1)*(1+1+1), so a(6) = 5.
For n = 32, 32 = 11*(1+1+1)-1, so a(32) = 6.
For n = 37, 37 = 111/(1+1+1), so a(37) = 6.
For n = 78, 78 = 111-(11)*(1+1+1), so a(78) = 8.
		

Links

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

Crossrefs

Cf. A002275, A005245, A091333, A133344, A362626.

Formula

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

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