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A045953 Numbers n such that n^2 can be obtained from n by inserting an internal block of (contiguous) digits. 5
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)
OFFSET

1,3

COMMENTS

All terms of this sequence appear in A086457. - Jeremy Gardiner, Jul 20 2003

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..100

J. Knoderer, An Interesting Sequence of Numbers

EXAMPLE

95^2 = 9025 (insert '02' inside '95').

PROG

(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)

-- Reinhard Zumkeller, Jul 27 2011

CROSSREFS

Cf. A046851, A008851, A018834.

Sequence in context: A262229 A086457 A046851 * A136830 A153069 A178569

Adjacent sequences:  A045950 A045951 A045952 * A045954 A045955 A045956

KEYWORD

base,nonn,nice,easy

AUTHOR

John "MazeMan" Knoderer (Webmaster(AT)Mazes.com)

STATUS

approved

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Last modified December 4 13:35 EST 2016. Contains 278750 sequences.