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A156977
Numbers n such that n^2 contains every decimal digit exactly once.
15
32043, 32286, 33144, 35172, 35337, 35757, 35853, 37176, 37905, 38772, 39147, 39336, 40545, 42744, 43902, 44016, 45567, 45624, 46587, 48852, 49314, 49353, 50706, 53976, 54918, 55446, 55524, 55581, 55626, 56532, 57321, 58413, 58455, 58554, 59403, 60984
OFFSET
1,1
COMMENTS
There are exactly 87 such numbers, none of them being prime.
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]
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..87 (full sequence)
S. C. Gould, Question 15734, The Educational Times, and Journal of the College of Preceptors 58 (1905), nr. 527 (March 1), p. 157; Solution 15734, Ibid., nr. 529 (May 1), p. 235.
FORMULA
a(n) = sqrt(A036745(n)).
MAPLE
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
MATHEMATICA
Select[Range[Floor@Sqrt@1023456789, Ceiling@Sqrt@9876543210], Sort@IntegerDigits[#^2] == Range[0, 9] &] (* Giovanni Resta, Mar 19 2013 *)
Select[Range[31992, 99381, 3], Union[DigitCount[#^2]]=={1}&] (* Harvey P. Dale, Jan 17 2022 *)
PROG
(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)
CROSSREFS
KEYWORD
fini,full,nonn,base
AUTHOR
Zak Seidov, Feb 20 2009
STATUS
approved