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A110380
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a(n) = min{p + q + r + ...} where p,q,r,... are distinct unary numbers - containing only ones, i.e., of the form (10^k - 1)/9 - formed by using a total of n ones.
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2
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1, 11, 12, 112, 122, 123, 1123, 1223, 1233, 1234, 11234, 12234, 12334, 12344, 12345, 112345, 122345, 123345, 123445, 123455, 123456, 1123456, 1223456, 1233456, 1234456, 1234556, 1234566, 1234567, 11234567, 12234567, 12334567, 12344567, 12345567, 12345667, 12345677
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OFFSET
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1,2
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COMMENTS
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The n-th term is the sum of m = A003056(n) repunits A000042, with the last n - m(m+1)/2 terms having one digit more than their index in that sum: see formula. The initial terms can also be described as numbers made of all of the digits 1 through m (m = 1, ..., 9) in increasing order, and at most one of these digits occurring twice in a row. - M. F. Hasler, Aug 08 2020
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LINKS
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FORMULA
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EXAMPLE
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Using n ones and only the + sign we get the following sums:
a(1) = 1;
a(2) = 11;
a(3) = 12 = 1 + 11;
a(4) = 112 = 1 + 111;
a(5) = 122 = 11 + 111;
a(6) = 123 = 1 + 11 + 111;
a(7) = 1123 = 1 + 11 + 1111;
a(8) = 1223 = 1 + 111 + 1111;
a(9) = 1233 = 11 + 111 + 1111.
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PROG
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(Haskell)
a110380 = drop 1 fn
where fn = 0 : 1 : concat (fn' 2)
fn' n = (map (+ones) (drop nv $ take (n + nv) fn)) : (fn' (n+1))
where ones = div (10^n -1) 9
nv = div ((n-1)*(n-2)) 2
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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