A046711 From the Bruck-Ryser theorem: numbers n == 1 or 2 (mod 4) which are also the sum of 2 squares.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

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), 88-93.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000161, A001481, A042963.

Programs

Haskell

a046711 n = a046711_list !! (n-1)
a046711_list = [x | x <- a042963_list, a000161 x > 0]
-- Reinhard Zumkeller, Aug 16 2011

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)& ]& (* Jean-François 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 *)

Python

from itertools import count, islice
from sympy import factorint
def A046711_gen(): # generator of terms
    return filter(lambda n:0 < n & 3 < 3 and all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n).items()),count(0))
A046711_list = list(islice(A046711_gen(),30)) # Chai Wah Wu, Jun 28 2022

Extensions

More terms from James Sellers