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A054038
Numbers k such that k^2 contains every digit at least once.
31
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
OFFSET
1,1
COMMENTS
There are 87 terms < 10^5; these are the n such that n^2 uses each digit exactly once. - David Wasserman, Feb 03 2005
The squares in this sequence are in A190682. - Bruno Berselli, May 23 2011
REFERENCES
J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 239 pp. 39; 178, Ellipses Paris 2004.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 4866 terms from Klaus Brockhaus)
MAPLE
f := []; for i from 0 to 200 do if nops({op(convert(i^2, base, 10))})=10 then f := [op(f), i] fi; od; f;
MATHEMATICA
A050278 = Select[FromDigits@#&/@Permutations[Range[0, 9], {10}], # > 10^9 &]; Sqrt[Select[A050278, IntegerQ[Sqrt[#]] &]] (* Alonso del Arte, Jun 18 2011, based on a program by Robert G. Wilson v *)
Select[Sqrt[#]&/@FromDigits/@Select[Permutations[Range[0, 9]], #[[1]]>0&], IntegerQ] (* Harvey P. Dale, May 26 2016 *)
PROG
(Magma) IsA054038:=func< n | Seqset(Intseq(n^2)) eq {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} >; [ n: n in [1..60000] | IsA054038(n) ]; // Klaus Brockhaus, May 16 2011
(PARI) is(n)=#vecsort(Vec(Str(n^2)), , 8)==10 \\ Charles R Greathouse IV, Jun 18 2011
(Python)
def ok(n): return len(set(str(n**2))) == 10
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Dec 23 2022
KEYWORD
nonn,base
AUTHOR
Asher Auel, Feb 28 2000
EXTENSIONS
More terms from David Wasserman, Feb 03 2005
STATUS
approved