OFFSET
1,1
COMMENTS
No point with integer distance to all four corners is known.
The sequence only contains even values because an odd-sided square centered at the origin has corners with non-integer coordinates, which cannot be at integer distance from interior lattice points. If the square instead of being centered at the origin has a corner on the origin, then the resulting sequence is A260549. - Giovanni Resta, Jul 29 2015
LINKS
Yasushi Ieno, Other special cases of a square problem, arXiv:2111.02888 [math.GM], 2021.
Yang Ji, Several special cases of a square problem, arXiv:2105.05250 [math.GM], 2021.
G. Shute and K. L. Yocom, Problem 966. Seven integral distances, Math. Mag. 50, 166 (1977).
UnsolvedProblems Web Site, Rational Distance
EXAMPLE
With n = side length, we find an a,b such that a^2 + b^2 = d1^2, a^2 + (n-b)^2 = d2^2, b^2 + (n-a)^2 = d3^2, (n-a)^2 + (n-b)^2 = d4^2 is true in integers for three of these four equations. n = 52 is the first, with a=7 and b=24.
PROG
(PARI) has(n)=for(a=1, n-1, for(b=a, n-1, if(issquare(norml2([a, b])) + issquare(norml2([n-a, b])) + issquare(norml2([a, n-b])) + issquare(norml2([n-a, n-b])) > 2, return(1)))); 0
is(n)=sumdiv(n, d, has(d))==1 \\ Charles R Greathouse IV, Jul 28 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Mark Underwood, Aug 08 2012
EXTENSIONS
Data corrected and name improved by Mark Underwood, Jul 28 2015
a(7)-a(39) from Giovanni Resta, Jul 29 2015
STATUS
approved