|
| |
|
|
A111213
|
|
Difference between the closest squares surrounding prime p is prime.
|
|
0
| |
|
|
3, 3, 5, 5, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 17, 17, 19, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 41, 41, 41, 43, 43, 43, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,1
|
|
|
COMMENTS
| Conjecture: The number of terms in this sequence is infinite.
|
|
|
FORMULA
| Let p be a prime number and r = floor(sqrt(p)). Then the closest surrounding squares of p are r^2 and (r+1)^2. So d = (r+1)^2 - r^2 = 2r+1. If if d is prime then list d.
|
|
|
EXAMPLE
| 29 is a prime number. 5^2 and 6^2 are the closest squares surrounding 29. Now
the difference, 36-25 = 11 is prime so 11 is in the table.
|
|
|
PROG
| (PARI) surrsqpr(n) = { local(x, y, j, r, d); forprime(x=2, n, r=floor(sqrt(x)); d=r+r+1; if(isprime(d), print1(d", ") ) ) }
|
|
|
CROSSREFS
| Sequence in context: A073737 A187072 A133908 * A095878 A077381 A157966
Adjacent sequences: A111210 A111211 A111212 * A111214 A111215 A111216
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Nov 12 2005
|
| |
|
|
