A014563 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) contained in the digits of a(n+1)^2, with a(0)=1.

1, 4, 13, 14, 31, 36, 54, 96, 113, 311, 487, 854, 1036, 1277, 1646, 3214, 8351, 10456, 11414, 11536, 11563, 17606, 17813, 30287, 36786, 41544, 54927, 56547, 56586, 57363, 62469, 62634, 72813, 72897, 76944, 78345, 95061, 97944, 100963, 101944

Offset: 0

Author

Marc Paulhus, Jan 29 2002

Keywords

• base
• nonn
• nice

Comments

Probably infinite. - David W. Wilson, Jan 29 2002

Examples

			13^2 = 169 and 14 is the next smallest number whose square (in this case 196) contains the digits 1,6,9.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

If "contained in" is replaced by "properly contained in" we get A065297.

Cf. A066825, A067633, A067634, A067635, A065297.

Cf. A000290, A000196.

Programs

Haskell

import Data.List ((\\))
a014563 n = a014563_list !! n
a014563_list = 1 : f 1 (drop 2 a000290_list) where
   f x (q:qs) | null $ xs \\ (show q) = y : f y qs
              | otherwise             = f x qs
              where y = a000196 q; xs = show (x * x)
-- Reinhard Zumkeller, Nov 22 2012

Mathematica

snd[n_]:=Module[{k=n+1},While[!AllTrue[Select[Transpose[{DigitCount[n^2],
DigitCount[k^2]}],#[[1]]>0&],#[[1]]<=#[[2]]&],k++];k]; NestList[ snd,1,40] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 21 2016 *)