|
| |
|
|
A129592
|
|
The smallest in a triple of three consecutive primes such that the ceiling of the square root of their sums-of-squares is prime.
|
|
0
| |
|
|
2, 7, 13, 43, 53, 59, 127, 241, 271, 317, 331, 349, 367, 439, 487, 491, 607, 659, 719, 733, 757, 773, 821, 857, 881, 929, 971, 1087, 1193, 1259, 1289, 1303, 1409, 1427, 1453, 1607, 1663, 1693, 1723, 1747, 1789, 1949, 2053, 2087, 2089, 2131, 2251, 2333, 2393, 2467, 2549, 2633, 2671, 2719
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Can three squares with consecutive prime sides prime(i), i=k,..k+2, be contained/morphed in a larger square also with prime sides just slightly greater than required?
The areas are the squares of the prime sides; the total area is their sum prime(k)^2+prime(k+1)^2+prime(k+2)^2,
and pulling the square root is the diagonal of the hosting square. The sequence lists the first, prime(k), if this diagonal (rounded up) is a prime number,
indicating that a rather tight enclosing square with (again) a prime side length can be found.
|
|
|
FORMULA
| {A000040(n): ceil(sqrt(A133529(n))) in A000040}. - R. J. Mathar, Jul 10 2011
|
|
|
EXAMPLE
| Take 13,17,19 with summed squares 169+289+361=819 = A133529(6). The square root is approximately 28.6 and rounding up to 29 yields a prime, so 13 is placed
in the sequence.
|
|
|
CROSSREFS
| Sequence in context: A051748 A086904 A026555 * A153136 A178607 A127487
Adjacent sequences: A129589 A129590 A129591 * A129593 A129594 A129595
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| J. M. Bergot (thekingfishb(AT)yahoo.ca), May 30 2007
|
|
|
EXTENSIONS
| Edited and extended by R. J. Mathar, Jul 10 2011
|
| |
|
|
