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

1,3

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

Links

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

J. Knoderer, What number comes next? (an interesting sequence)

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: A331604 A086457 A046851 * A136830 A153069 A332703

Adjacent sequences: A045950 A045951 A045952 * A045954 A045955 A045956

Keyword

base,nonn,nice,easy

Author

John William Knoderer

Status

approved