|
Search: id:A145009
|
|
|
| A145009 |
|
Triangle read by rows: array of odd integers found in |A144912| with axes b = {4, 6, 8, ...} and n = {b^2, b^4, b^6, ...}. |
|
+0
1
|
|
| 7, 13, 13, 19, 23, 19, 25, 33, 33, 25, 31, 43, 47, 43, 31, 37, 53, 61, 61, 53, 37, 43, 63, 75, 79, 75, 63, 43, 49, 73, 89, 97, 97, 89, 73, 49, 55, 83, 103, 115, 119, 115, 103, 83, 55, 61, 93, 117, 133, 141, 141, 133, 117, 93, 61
(list; table; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
The complete array can be defined as 6(x + y) + 4xy + 7.
Values along the edges are given by 6x + 7 and thus include the larger member of every twin prime pair except 5. The smaller member, 6x + 5, is adjacent in |A144912|.
Taking the origin to be z = 1, the main diagonal is given by 4z^2 + 4z - 1 (A073577).
Sums along antidiagonals are given by z(2z^2 + 12z + 7) / 3.
Contribution from Reikku Kulon (reikku(AT)gmail.com), Sep 29 2008: (Start)
Any entry in the triangle can be produced from the two terms diagonally above or below and the edges can be found by taking the odd numbers as the "missing" values, starting from 1. If the terms are denoted:
.. a0 .. ...
a1 .. a2 ...
.. a3 .. ...
then:
a0 = (a1 + a2 + 4) / 2 - sqrt(a1^2 + 8 * a1 - 2 * a1 * a2 + 8 * a2 + a2^2 + 48) / 2;
a3 = (a1 + a2 + 4) / 2 + sqrt(a1^2 + 8 * a1 - 2 * a1 * a2 + 8 * a2 + a2^2 + 48) / 2. (End)
|
|
CROSSREFS
|
Cf. A000040, A006512, A073577, A144912
Sequence in context: A115858 A114389 A135555 this_sequence A090229 A057930 A013651
Adjacent sequences: A145006 A145007 A145008 this_sequence A145010 A145011 A145012
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Reikku Kulon (reikku(AT)gmail.com), Sep 28 2008
|
|
|
Search completed in 0.005 seconds
|
