OFFSET
1,1
COMMENTS
The number m with no repeated digits has an exclusionary square m^2 if the latter is made up of digits not appearing in m. For the corresponding exclusionary squares see A112735.
a(49) = 567 and a(68) = 854 are the only two numbers k such that the equation k^2 = m uses only once each of the digits 1 to 9 (reference David Wells). Exactly: 567^2 = 321489, and, 854^2 = 729316. - Bernard Schott, Dec 20 2021
REFERENCES
H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, 1997, page 144, entry 567.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..142 (full sequence)
EXAMPLE
409^2 = 167281 and the square 167281 is made up of digits not appearing in 409, hence 409 is a term.
MATHEMATICA
Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ]]] == Length[IntegerDigits[ # ]] &] - Tanya Khovanova, Dec 25 2006
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Lekraj Beedassy, Sep 16 2005
EXTENSIONS
More terms from Tanya Khovanova, Dec 25 2006
STATUS
approved