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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 /, where fractions are allowed as intermediate results.
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%I #17 Apr 30 2023 02:14:22

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

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

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

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

%H Michael S. Branicky, <a href="/A362626/b362626.txt">Table of n, a(n) for n = 1..10000</a>

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

%e a(111) = 3.

%Y Cf. A002275, A005245, A362471.

%K nonn,base

%O 1,2

%A _Yifan Xie_, _Haochen Mi_ and _Michael S. Branicky_, Apr 28 2023