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A045953
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Numbers m such that m^2 can be obtained from m by inserting an internal block of (contiguous) digits.
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5
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0, 1, 10, 11, 95, 96, 100, 101, 125, 976, 995, 996, 1000, 1001, 1025, 1376, 9625, 9976, 9995, 9996, 10000, 10001, 10025, 10376, 10625, 99376, 99625, 99976, 99995, 99996, 100000, 100001, 100025, 100376, 100625, 109376, 990625, 999376, 999625, 999976
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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It seems that for any nonnegative integer k the number of k-digit terms is 2k. - Ivan N. Ianakiev, Aug 17 2021
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LINKS
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EXAMPLE
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95^2 = 9025 (insert '02' inside '95').
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PROG
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(Haskell)
import Data.List (isPrefixOf, inits, isSuffixOf, tails)
a045953 n = a045953_list !! (n-1)
a045953_list = filter chi a008851_list where
chi n = (x == y && xs `isSub'` ys) where
x:xs = show $ div n 10
y:ys = show $ div (n^2) 10
isSub' us vs = any id $ zipWith (&&)
(map (`isPrefixOf` vs) $ inits us)
(map (`isSuffixOf` vs) $ tails us)
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CROSSREFS
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KEYWORD
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base,nonn,nice,easy
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AUTHOR
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John "MazeMan" Knoderer (Webmaster(AT)Mazes.com)
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STATUS
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approved
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