|
|
A084105
|
|
Middle q of three consecutive primes p,q,r, such that one adjacent prime is near, the other is far and the ratio of the differences (whichever of (r-q)/(q-p) or (q-p)/(r-q) is greater than 1) sets a record.
|
|
4
|
|
|
3, 29, 113, 139, 199, 523, 1151, 1669, 2971, 6947, 10007, 16141, 25471, 40639, 79699, 102761, 173359, 265621, 404851, 838249, 1349533, 1562051, 6371537, 7230479, 27980987, 42082303, 53231051, 70396589, 192983851, 253878617, 390932389, 465828731, 516540163, 1692327137
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Are there entries other than a(3) for which the smaller difference exceeds 2?
|
|
LINKS
|
|
|
EXAMPLE
|
a(3) = 113 because the ratio (113-109)/(127-113) = 2/7 = 0.28571.. is smaller than the previous minimum produced by (31-29)/(29-23) = 1/3 = 0.33333...
|
|
PROG
|
(PARI) a084105(limit)={my(p1=2, p2=3, r=0); forprime(p3=5, limit, my(q=max((p2-p1)/(p3-p2), (p3-p2)/(p2-p1))); if(q>r, r=q; print1(p2, ", ")); p1=p2; p2=p3)};
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|