|
Search: id:A111693
|
|
|
| A111693 |
|
The number system may be represented by linearly stringing together all the square domains. The number of the domain is given by r. it is noted that this has the same value as the circuit number in the Ellerstein square spiral. One below each odd square is a zero centered octagonal number, which is divisible by 8. The value of this is eight times a triangle number. It may be seen that there are r octades in each square domain. The sequence is the first prime number in the first octade of each square domain. |
|
+0
1
|
|
| 3, 11, 29, 53, 83, 127, 173, 227, 293, 367, 443
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Other work is in progress where the distribution of primes in successive octads is being calculated to see what pattern if any emerges. These will be published when they are available. It is noted that each square domain has 8 sectors of length r besides the r octades of length 8 which are intertwined.
|
|
REFERENCES
|
Stuart M. Ellerstein, J. Recreational Mathematics, Vol. 29,3, pp. 188 - 189,1998. Stuart M. Ellerstein, J. Recreational Mathematics, Vol. 30,4, pp. 246 - 250,1999- 2000.
|
|
EXAMPLE
|
For the sixth square domain r=6. The ZCON is 120, which is 8x15, since it is
8x 6(6-1)/2, and the first prime is 8x15 + 7. The odd square is (2r -1)^2 = 121.
|
|
CROSSREFS
|
Sequence in context: A018743 A077279 A111227 this_sequence A100032 A069350 A053845
Adjacent sequences: A111690 A111691 A111692 this_sequence A111694 A111695 A111696
|
|
KEYWORD
|
easy,nonn,uned
|
|
AUTHOR
|
Stuart M. Ellerstein (ellerstein(AT)aol.com), Jun 17 2006
|
|
|
Search completed in 0.002 seconds
|
