

A046711


From the BruckRyser theorem: numbers n == 1 or 2 (mod 4) which are also the sum of 2 squares.


4



1, 2, 5, 9, 10, 13, 17, 18, 25, 26, 29, 34, 37, 41, 45, 49, 50, 53, 58, 61, 65, 73, 74, 81, 82, 85, 89, 90, 97, 98, 101, 106, 109, 113, 117, 121, 122, 125, 130, 137, 145, 146, 149, 153, 157, 162, 169, 170, 173, 178, 181, 185, 193, 194, 197, 202, 205, 218, 221, 225
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

If n = 1, 2 (mod 4) and the squarefree part of n is divisible by a prime p = 3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n exists, and n= 1 or 2 (mod 4), then n is the sum of two squares.  Jonathan Vos Post, Apr 17 2011
Intersection of A001481 and A042963; A000161(a(n)) > 0.  Reinhard Zumkeller, Feb 14 2012


REFERENCES

M. Hall, Jr., Combinatorial Theory, Theorem 12.3.2.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
R. H. Bruck and H. J. Ryser, The nonexistence of certain projective planes, Canad. J. Math., 1 (1949), 8893.
Index entries for sequences related to sums of squares


MATHEMATICA

max = 225; Flatten[ Table[ a^2 + b^2, {a, 0, Sqrt[max]}, {b, a, Sqrt[max  a^2]}], 1] // Union // Select[#, (1 <= Mod[#, 4] <= 2)& ]& (* JeanFrançois Alcover, Sep 13 2012 *)
With[{max=15}, Select[Select[Total/@Tuples[Range[0, max]^2, 2], MemberQ[ {1, 2}, Mod[ #, 4]]&]//Union, #<=max^2&]] (* Harvey P. Dale, Jan 14 2017 *)


PROG

(Haskell)
a046711 n = a046711_list !! (n1)
a046711_list = [x  x < a042963_list, a000161 x > 0]
 Reinhard Zumkeller, Aug 16 2011


CROSSREFS

Cf. A000161, A001481, A042963.
Sequence in context: A078360 A114995 A047619 * A191171 A191776 A095347
Adjacent sequences: A046708 A046709 A046710 * A046712 A046713 A046714


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from James A. Sellers


STATUS

approved



