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

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

Offset: 1

Author

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

Keywords

• base
• nonn
• nice
• easy

Comments

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

It seems that for any nonnegative integer k the number of k-digit terms is 2k. - Ivan N. Ianakiev, Aug 17 2021

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..100
• J. Knoderer, What number comes next? (an interesting sequence)

Crossrefs

Cf. A046851, A008851, A018834.

Programs

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