A046712 From the Bruck-Ryser theorem: n == 1 or 2 (mod 4) which are not the sum of 2 squares.

6, 14, 21, 22, 30, 33, 38, 42, 46, 54, 57, 62, 66, 69, 70, 77, 78, 86, 93, 94, 102, 105, 110, 114, 118, 126, 129, 133, 134, 138, 141, 142, 150, 154, 158, 161, 165, 166, 174, 177, 182, 186, 189, 190, 198, 201, 206, 209, 210, 213, 214, 217, 222, 230, 237, 238

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

Intersection of A022544 and A046712. - Reinhard Zumkeller, Aug 16 2011

References

• M. Hall, Jr., Combinatorial Theory, Wiley, New York, 1986, see 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), 88-93.
• Eric Weisstein's World of Mathematics, Bruck-Ryser-Chowla Theorem.
• Wikipedia, Bruck-Ryser-Chowla theorem.
• Index entries for sequences related to sums of squares

Programs

Haskell

a046712 n = a046712_list !! (n-1)
a046712_list = filter ((`elem` [1,2]) . (`mod` 4)) a022544_list
-- Reinhard Zumkeller, Aug 16 2011

Mathematica

Select[Range[240], (Mod[#, 4] == 1 || Mod[#, 4] == 2) && PowersRepresentations[#, 2, 2] == {} & ] (* Jean-François Alcover, Aug 30 2011 *)
Select[Range[250],MemberQ[{1,2},Mod[#,4]]&&SquaresR[2,#]==0&] (* Harvey P. Dale, Apr 01 2015 *)

Extensions

More terms from James Sellers