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%I #32 Dec 21 2022 12:07:19
%S 32043,32286,33144,35172,35337,35757,35853,37176,37905,38772,39147,
%T 39336,40545,42744,43902,44016,45567,45624,46587,48852,49314,49353,
%U 50706,53976,54918,55446,55524,55581,55626,56532,57321,58413,58455,58554,59403,60984
%N Numbers n such that n^2 contains every decimal digit exactly once.
%C There are exactly 87 such numbers, none of them being prime.
%C Since 0 + 1 +...+ 9 = 5*9, every pandigital number is divisible by 9, hence every term of this sequence is divisible by 3 and so cannot be a prime. - _Giovanni Resta_, Mar 19 2013 [Comment expanded by _N. J. A. Sloane_, Jan 15 2022]
%H Giovanni Resta, <a href="/A156977/b156977.txt">Table of n, a(n) for n = 1..87</a> (full sequence)
%H S. C. Gould, <a href="https://archive.org/details/educationaltimes58educ/page/156/mode/1up?view=theater">Question 15734</a>, The Educational Times, and Journal of the College of Preceptors 58 (1905), nr. 527 (March 1), p. 157; <a href="https://archive.org/details/educationaltimes58educ/page/235/mode/1up?view=theater">Solution 15734</a>, Ibid., nr. 529 (May 1), p. 235.
%F a(n) = sqrt(A036745(n)).
%p lim:=floor(sqrt(9876543210)): for n from floor(sqrt(1023456789)) to lim do d:=[op(convert(n^2, base, 10))]: pandig:=true: for k from 0 to 9 do if(numboccur(k, d)<>1)then pandig:=false: break: fi: od: if(pandig)then printf("%d, ",n): fi: od: # _Nathaniel Johnston_, Jun 22 2011
%t Select[Range[Floor@Sqrt@1023456789, Ceiling@Sqrt@9876543210], Sort@IntegerDigits[#^2] == Range[0, 9] &] (* _Giovanni Resta_, Mar 19 2013 *)
%t Select[Range[31992,99381,3],Union[DigitCount[#^2]]=={1}&] (* _Harvey P. Dale_, Jan 17 2022 *)
%o (Magma) [n: n in [Floor(Sqrt(1023456789))..Ceiling(Sqrt(9876543210))] | Set(Intseq(n^2)) eq {0..9}]; // _Bruno Berselli_, Mar 19 2013 (after Giovanni Resta)
%Y Cf. A036745, A054037, A054038.
%K fini,full,nonn,base
%O 1,1
%A _Zak Seidov_, Feb 20 2009
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