|
|
A343195
|
|
a(n) is the parameter c in the three parameter description of 3 X 3 magic squares of consecutive primes (see comment).
|
|
4
|
|
|
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -6, 6, 24, 6, 6, 6, -18, 6, 6, -18, 6, 6, -18, 6, -18, 6, 24, 6, 6, -6, 6, -18, 6, 24, 6, 6, 6, 6, -18, 6, 6, -54, -18, 6, 6, 6, -18, 12, 6, 78, 12, -18, 24, 24, -24, 6, 6, 6, 6, 6, 24, 6, 6, 6, 6, 12, 12, 24, 6, 6, 24, -18, 6, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Each 3 X 3 magic square of consecutive primes can be described by three parameters: p1, b and c, where p1 is the smallest prime in the magic square, b > 0 and c > -b; the magic square is then given by:
+----------+----------+----------+
| p1+5b+2c | p1 | p1+4b+c |
+----------+----------+----------+
| p1+2b | p1+3b+c | p1+4b+2c |
+----------+----------+----------+
| p1+2b+c | p1+6b+2c | p1+b |
+----------+----------+----------+
If c > 0, the magic square is of type 1; if -b < c < 0, the magic square is of type 2. If the consecutive primes are given by p1, p2, ..., p9 (in increasing order), the magic square types are given by:
Type 1 Type 2
+----+----+----+ +----+----+----+
| p8 | p1 | p6 | | p8 | p1 | p7 |
+----+----+----+ +----+----+----+
| p3 | p5 | p7 | | p4 | p5 | p6 |
+----+----+----+ +----+----+----+
| p4 | p9 | p2 | | p3 | p9 | p2 |
+----+----+----+ +----+----+----+
|
|
LINKS
|
|
|
FORMULA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|