cp's OEIS Frontend

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

%I A045953 #21 Aug 27 2021 16:59:56
%S A045953 0,1,10,11,95,96,100,101,125,976,995,996,1000,1001,1025,1376,9625,
%T A045953 9976,9995,9996,10000,10001,10025,10376,10625,99376,99625,99976,99995,
%U A045953 99996,100000,100001,100025,100376,100625,109376,990625,999376,999625,999976
%N A045953 Numbers m such that m^2 can be obtained from m by inserting an internal block of (contiguous) digits.
%C A045953 All terms of this sequence appear in A086457. - _Jeremy Gardiner_, Jul 20 2003
%C A045953 It seems that for any nonnegative integer k the number of k-digit terms is 2k. - _Ivan N. Ianakiev_, Aug 17 2021
%H A045953 Reinhard Zumkeller, <a href="/A045953/b045953.txt">Table of n, a(n) for n = 1..100</a>
%H A045953 J. Knoderer, <a href="https://web.archive.org/web/20090910061731/http://www.mazes.com/sequence.html">What number comes next? (an interesting sequence)</a>
%e A045953 95^2 = 9025 (insert '02' inside '95').
%o A045953 (Haskell)
%o A045953 import Data.List (isPrefixOf, inits, isSuffixOf, tails)
%o A045953 a045953 n = a045953_list !! (n-1)
%o A045953 a045953_list = filter chi a008851_list where
%o A045953    chi n = (x == y && xs `isSub'` ys) where
%o A045953       x:xs = show $ div n 10
%o A045953       y:ys = show $ div (n^2) 10
%o A045953       isSub' us vs = any id $ zipWith (&&)
%o A045953                               (map (`isPrefixOf` vs) $ inits us)
%o A045953                               (map (`isSuffixOf` vs) $ tails us)
%o A045953 -- _Reinhard Zumkeller_, Jul 27 2011
%Y A045953 Cf. A046851, A008851, A018834.
%K A045953 base,nonn,nice,easy
%O A045953 1,3
%A A045953 John "MazeMan" Knoderer (Webmaster(AT)Mazes.com)