|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
REFERENCES
|
J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 239 pp. 39; 178, Ellipses Paris 2004.
|
|
LINKS
|
|
|
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
|
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
(Python)
def ok(n): return len(set(str(n**2))) == 10
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|