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A328173
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Numbers k such that decimal expansion of k^2 can be split into two parts whose sum is a number with repeated digits.
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1
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4, 5, 6, 9, 10, 11, 20, 22, 30, 33, 44, 55, 57, 66, 77, 99, 100, 111, 159, 171, 200, 222, 300, 333, 444, 555, 666, 704, 889, 999, 1000, 1111, 1149, 1578, 1755, 2000, 2025, 2222, 2618, 3000, 3111, 3333, 6666, 7777, 9999, 10000, 11111, 20000, 22222, 22568, 22972, 30000, 30297, 33333
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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EXAMPLE
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4^2 = 16, 1 + 6 = 7.
5^2 = 25, 2 + 5 = 7.
6^2 = 36, 3 + 6 = 9.
9^2 = 81, 8 + 1 = 9.
10^2 = 100, 1 + 0 = 1.
11^2 = 121, 1 + 21 = 22.
20^2 = 400, 4 + 0 = 4.
22^2 = 484, 4 + 84 = 88.
30^2 = 900, 9 + 0 = 9.
33^2 = 1089, 10 + 89 = 99.
44^2 = 1936, 19 + 36 = 55.
55^2 = 3025, 30 + 25 = 55.
57^2 = 3249, 324 + 9 = 333.
66^2 = 4356, 43 + 56 = 99.
77^2 = 5929, 59 + 29 = 88.
99^2 = 9801, 98 + 1 = 99.
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PROG
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(Ruby)
def A(str)
(0..str.size - 2).any?{|i| (str[0..i].to_i + str[i + 1..-1].to_i).to_s.split('').uniq.size == 1}
end
p (0..10 ** 4).select{|i| A((i * i).to_s)}
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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