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

1,3

Comments

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

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

Links

Table of n, a(n) for n=1..67.

Example

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.

Sequence in context: A035261 A047351 A242937 * A028951 A035248 A190244

Adjacent sequences: A247976 A247977 A247978 * A247980 A247981 A247982

Keyword

easy,nonn

Author

Alonso del Arte, Sep 28 2014

Status

approved