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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Asher Auel, Feb 28 2000
EXTENSIONS
More terms from David Wasserman, Feb 03 2005
STATUS
approved