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A046712
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From the Bruck-Ryser theorem: n == 1 or 2 (mod 4) which are not the sum of 2 squares.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 a022544 and A046712. [Reinhard Zumkeller, Aug 16 2011]
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REFERENCES
| R. H. Bruck and H. J. Ryser, The nonexistence of certain projective planes, Canad. J. Math., 1 (1949), 88-93.
M. Hall, Jr., Combinatorial Theory, Theorem 12.3.2.
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LINKS
| Index entries for sequences related to sums of squares
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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MATHEMATICA
| Select[Range[240], (Mod[#, 4] == 1 || Mod[#, 4] == 2) && PowersRepresentations[#, 2, 2] == {} & ] (* From Jean-François Alcover, Aug 30 2011 *)
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PROG
| (Haskell)
a046712 n = a046712_list !! (n-1)
a046712_list = filter ((`elem` [1, 2]) . (`mod` 4)) a022544_list
-- Reinhard Zumkeller, Aug 16 2011
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CROSSREFS
| Sequence in context: A064708 A064709 A118129 * A162823 A020171 A122784
Adjacent sequences: A046709 A046710 A046711 * A046713 A046714 A046715
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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