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

1,2

Comments

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

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

Links

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

Example

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

Crossrefs

Cf. A002275, A005245, A362471.

Sequence in context: A007599 A330881 A279317 * A362471 A154940 A133344

Adjacent sequences: A362623 A362624 A362625 * A362627 A362628 A362629

Keyword

nonn,base

Author

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

Status

approved