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a(n) is the smallest number of 1's used in expressing n as a calculation containing only decimal repunits and operators +, -, * and /.
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%I #49 Apr 30 2023 02:01:21

%S 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,

%T 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,

%U 8,9,9,8,9,8,9,9,8,8,9,8,8,9,10,9,9,9,8,7,7

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

%C Here, fractions are not allowed as intermediate results.

%C 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

%H Michael S. Branicky, <a href="/A362471/b362471.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%e For n = 6, 6 = (1+1)*(1+1+1), so a(6) = 5.

%e For n = 32, 32 = 11*(1+1+1)-1, so a(32) = 6.

%e For n = 37, 37 = 111/(1+1+1), so a(37) = 6.

%e For n = 78, 78 = 111-(11)*(1+1+1), so a(78) = 8.

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

%K nonn,base

%O 1,2

%A _Yifan Xie_, _Haochen Mi_ and _Michael S. Branicky_, Apr 21 2023