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

1,2

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

Links

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

Formula

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

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

Example

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.

Crossrefs

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

Sequence in context: A330881 A279317 A362626 * A154940 A133344 A323727

Adjacent sequences: A362468 A362469 A362470 * A362472 A362473 A362474

Keyword

nonn,base

Author

Yifan Xie, Haochen Mi and Michael S. Branicky, Apr 21 2023

Status

approved