|
Search: id:A164554
|
|
| |
|
| 2, 71, 101, 181, 239, 241, 269, 349, 373, 409, 419, 433, 439, 491, 593, 599, 601, 607, 647, 653, 659, 823, 827, 857, 947, 1021, 1031, 1061, 1063, 1091, 1103, 1301, 1427, 1429, 1447, 1451, 1489, 1553, 1559, 1567, 1601, 1607, 1609, 1789, 1867, 1871, 1913, 1999, 2003
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
For every n>=1, A104272(n) >= A080359(n), and the sequence shows where the inequality becomes an equality.
Let prime(m) < a(n)/2 < prime(m+1); then primes p<q exist such that p is in the interval (2*Prime(m), a(n))
and such that q is in the interval (a(n), 2*Prime(m+1)).
|
|
LINKS
|
V. Shevelev, On critical small intervals containing primes, arXiv:0908.2319 [math.NT] [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Aug 20 2009]
|
|
EXAMPLE
|
a(2)=71, such that 31<71/2<37, and we see that p=67 is in interval (62, 71) and q=73 is in interval (71, 74).
|
|
CROSSREFS
|
A104272 A080359 A164368 A164333 A164288 A164294
|
|
KEYWORD
|
nonn,new
|
|
AUTHOR
|
Vladimir Shevelev (shevelev(AT)bgu.ac.il), Aug 15 2009
|
|
EXTENSIONS
|
Terms beyond 659 from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 17 2009
|
|
|
Search completed in 0.002 seconds
|
