The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A096315 Numbers n such that the n-dimensional integer lattice Z^n contains n+1 equidistant points (i.e., the vertices of a regular n-simplex). 1
 1, 3, 7, 8, 9, 11, 15, 17, 19, 23, 24, 25, 27, 31, 33, 35, 39, 43, 47, 48, 49, 51, 55, 57, 59, 63, 67, 71, 73, 75, 79, 80, 81, 83, 87, 89, 91, 95, 97, 99, 103, 105, 107, 111, 115, 119, 120, 121, 123, 127, 129, 131, 135, 139, 143, 145, 147, 151, 155, 159, 161, 163, 167 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Schoenberg proved that a regular n-simplex can be inscribed in Z^n in the following cases and no others: (1) n is even and n+1 is a square; (2) n == 3 (mod 4); (3) n == 1 (mod 4) and n+1 is the sum of two squares. LINKS I. J. Schoenberg, Regular Simplices and Quadratic Forms, J. London Math. Soc. 12 (1937) 48-55. EXAMPLE There is no equilateral triangle in the plane whose vertices have integer coordinates, so 2 is not on the list. But there is a regular tetrahedron in space whose vertices have integer coordinates, namely (0,0,0), (0,1,1), (1,0,1), (1,1,0), hence 3 is on the list. MAPLE select(n->(is(n, even) and issqr(n+1)) or (n mod 4 = 3) or ((n mod 4 = 1) and (numtheory[sum2sqr](n+1)<>[])), [ \$1..200]); CROSSREFS Sequence in context: A122987 A047530 A265350 * A286395 A112680 A096079 Adjacent sequences:  A096312 A096313 A096314 * A096316 A096317 A096318 KEYWORD easy,nonn AUTHOR David Radcliffe, Aug 01 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 17 09:54 EST 2020. Contains 330949 sequences. (Running on oeis4.)