cp's OEIS Frontend

A112736 Numbers whose square is exclusionary.

%I A112736 #21 Aug 09 2025 21:04:58
%S A112736 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 A112736 94,157,158,173,187,192,194,209,237,238,247,253,257,259,307,314,349,
%U A112736 359,409,437,459,467,547,567,612,638,659,672,673,689,712,729,738,739,749
%N A112736 Numbers whose square is exclusionary.
%C A112736 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 A112736 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 A112736 H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.
%D A112736 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, 1997, page 144, entry 567.
%H A112736 Giovanni Resta, <a href="/A112736/b112736.txt">Table of n, a(n) for n = 1..142</a> (full sequence)
%e A112736 409^2 = 167281 and the square 167281 is made up of digits not appearing in 409, hence 409 is a term.
%t A112736 Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ]]] == Length[IntegerDigits[ # ]] &] (* _Tanya Khovanova_, Dec 25 2006 *)
%Y A112736 Cf. A000290, A112321, A112735.
%Y A112736 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 A112736 nonn,base,fini,full
%O A112736 1,1
%A A112736 _Lekraj Beedassy_, Sep 16 2005
%E A112736 More terms from _Tanya Khovanova_, Dec 25 2006