A065297 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) properly contained in the digits of a(n+1)^2, with a(0)=1.

1, 4, 13, 36, 113, 487, 1036, 3214, 10456, 36786, 100963, 319656, 1001964, 3165969, 10001786, 31626854, 100013919, 316256807, 1000029656, 3162322481, 10000115537

Offset: 0

Author

Floor van Lamoen, Oct 29 2001

Keywords

• base
• nonn

Comments

Probably infinite and at least O(10^(n/2)). - David W. Wilson

Examples

			13^2 = 169 and 36 is the next smallest number whose square (in this case 1296) properly contains the digits 1,6,9.
		

Crossrefs

Cf. A050630, A050631, A048559, A050636, A065298, A014563, A066825.

Cf. A000290, A000196.

Programs

Haskell

import Data.List ((\\), sort)
a065297 n = a065297_list !! n
a065297_list = 1 : f 1 (drop 2 a000290_list) where
   f x (q:qs) | null (xs \\ sq) && sort xs /= sort sq = y : f y qs
              | otherwise                             = f x qs
              where y = a000196 q; sq = show q; xs = show (x * x)
-- Reinhard Zumkeller, Nov 22 2012

Extensions

More terms from Marc Paulhus, Jan 29 2002

More terms from David W. Wilson and Marc Paulhus, Feb 05 2002

a(19)-a(20) from Sean A. Irvine, Aug 26 2023