%I #18 Dec 20 2021 18:49:09

%S 2,3,4,7,8,9,17,18,24,29,34,38,39,47,53,54,57,58,59,62,67,72,79,84,92,

%T 94,157,158,173,187,192,194,209,237,238,247,253,257,259,307,314,349,

%U 359,409,437,459,467,547,567,612,638,659,672,673,689,712,729,738,739,749

%N Numbers whose square is exclusionary.

%C The number m with no repeated digits has an exclusionary square m^2 if the latter is made up of digits not appearing in m. For the corresponding exclusionary squares see A112735.

%C a(49) = 567 and a(68) = 854 are the only two numbers k such that the equation k^2 = m uses only once each of the digits 1 to 9 (reference David Wells). Exactly: 567^2 = 321489, and, 854^2 = 729316. - _Bernard Schott_, Dec 20 2021

%D H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, 1997, page 144, entry 567.

%H Giovanni Resta, <a href="/A112736/b112736.txt">Table of n, a(n) for n = 1..142</a> (full sequence)

%e 409^2 = 167281 and the square 167281 is made up of digits not appearing in 409, hence 409 is a term.

%t Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ]]] == Length[IntegerDigits[ # ]] &] - _Tanya Khovanova_, Dec 25 2006

%Y Cf. A000290, A112321, A112735.

%Y This is a subsequence of A029783 (Digits of n are not present in n^2) of numbers with all different digits. The sequence A059930 (Numbers n such that n and n^2 combined use different digits) is a subsequence of this sequence.

%K nonn,base,fini,full

%O 1,1

%A _Lekraj Beedassy_, Sep 16 2005

%E More terms from _Tanya Khovanova_, Dec 25 2006