A362471 - OEIS

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

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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.