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A247979 Numbers of the form x^2 + 7y^2 with x, y integers, or x^2/4 + 7y^2/4 with x, y odd integers. 0

%I

%S 0,1,2,4,7,8,9,11,14,16,18,21,22,23,25,28,29,32,36,37,43,44,46,49,50,

%T 53,56,58,63,64,67,71,72,74,77,79,81,86,88,92,98,99,100,106,107,109,

%U 112,113,116,121,126,127,128,134,137,142,144,148,149,151,154,158,161,162,163,169,172

%N Numbers of the form x^2 + 7y^2 with x, y integers, or x^2/4 + 7y^2/4 with x, y odd integers.

%C Norms of numbers in O_Q(sqrt(-7)).

%C A033207 and A045386 are subsets of this sequence. - _Colin Barker_, Sep 29 2014

%e 1/4 + 7/4 = 2, so 2 is in the sequence. (This also means 2 is composite in O_Q(sqrt(-7))).

%e 2^2 + 7 * 0^2 = 4, so 4 is in the sequence.

%e There is no way to express 5 as x^2 + 7y^2, nor as x^2/4 + 7y^2/4 if x and y are constrained to odd integers, hence 5 is not in the sequence. (This also means 5 is prime in O_Q(sqrt(-7)) and its norm is 25).

%Y Cf. A002481, A033207, A045386.

%K easy,nonn

%O 1,3

%A _Alonso del Arte_, Sep 28 2014

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Last modified August 5 19:54 EDT 2021. Contains 346488 sequences. (Running on oeis4.)