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, 1, 2, 4, 7, 8, 9, 11, 14, 16, 18, 21, 22, 23, 25, 28, 29, 32, 36, 37, 43, 44, 46, 49, 50, 53, 56, 58, 63, 64, 67, 71, 72, 74, 77, 79, 81, 86, 88, 92, 98, 99, 100, 106, 107, 109, 112, 113, 116, 121, 126, 127, 128, 134, 137, 142, 144, 148, 149, 151, 154, 158, 161, 162, 163, 169, 172

Offset: 1

Author

Alonso del Arte, Sep 28 2014

Keywords

• easy
• nonn

Comments

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

A033207 and A045386 are subsets of this sequence. - Colin Barker, Sep 29 2014

Examples

			1/4 + 7/4 = 2, so 2 is in the sequence. (This also means 2 is composite in O_Q(sqrt(-7))).
2^2 + 7 * 0^2 = 4, so 4 is in the sequence.
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).
		

Crossrefs

Cf. A002481, A033207, A045386.