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A002479 Numbers of form x^2 + 2y^2.
(Formerly M0547 N0197)
26
0, 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 17, 18, 19, 22, 24, 25, 27, 32, 33, 34, 36, 38, 41, 43, 44, 48, 49, 50, 51, 54, 57, 59, 64, 66, 67, 68, 72, 73, 75, 76, 81, 82, 83, 86, 88, 89, 96, 97, 98, 99, 100, 102, 107, 108, 113, 114, 118, 121, 123, 128, 129, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A positive number n belongs to this sequence if and only if every prime p == 5, 7 mod 8 dividing n occurs to an even power. - Sharon Sela (sharonsela(AT)hotmail.com), Mar 23 2002

Norms of numbers in Z[sqrt(-2)]. - Alonso del Arte, Sep 23 2014

REFERENCES

L. Euler, (E388) Vollstaendige Anleitung zur Algebra, Zweiter Theil, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 1, p. 421.

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 59.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

L. Euler, Vollstaendige Anleitung zur Algebra, Zweiter Teil.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

MATHEMATICA

q = 16; imax = q^2; Select[Union[Flatten[Table[x^2 + 2y^2, {y, 0, q/Sqrt[2]}, {x, 0, q}]]], # <= imax &] (* Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)

PROG

(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 1]%8>4 && f[i, 2]%2, return(0))); 1 \\ Charles R Greathouse IV, Nov 20 2012

(Haskell)

a002479 n = a002479_list !! (n-1)

a002479_list = 0 : filter f [1..] where

   f x = all (even . snd) $ filter ((`elem` [5, 7]) . (`mod` 8) . fst) $

                            zip (a027748_row x) (a124010_row x)

-- Reinhard Zumkeller, Feb 20 2014

CROSSREFS

Cf. A035251, A027748, A124010.

Complement of A097700.

For primes see A033203.

Sequence in context: A186541 A207432 A020900 * A010458 A218980 A084829

Adjacent sequences:  A002476 A002477 A002478 * A002480 A002481 A002482

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 24 09:23 EST 2014. Contains 249882 sequences.