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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.
7
1, 4, 13, 36, 113, 487, 1036, 3214, 10456, 36786, 100963, 319656, 1001964, 3165969, 10001786, 31626854, 100013919, 316256807, 1000029656, 3162322481, 10000115537
OFFSET
0,2
COMMENTS
Probably infinite and at least O(10^(n/2)). - David W. Wilson
EXAMPLE
13^2 = 169 and 36 is the next smallest number whose square (in this case 1296) properly contains the digits 1,6,9.
PROG
(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
KEYWORD
base,nonn
AUTHOR
Floor van Lamoen, Oct 29 2001
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
STATUS
approved