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.

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

Offset: 1

Author

Hugo Pfoertner, May 29 2003

Keywords

• nonn

Comments

Are there entries other than a(3) for which the smaller difference exceeds 2?

Examples

			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...
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..57
• Hugo Pfoertner, Maximally asymmetric prime triples, FORTRAN program

Crossrefs

Cf. A084106, A031132, A008996, A002386, A329158, A329159, A329160, A329161, A337489.

Programs

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)};
a084105(600000000) \\ Hugo Pfoertner, Sep 04 2020

Extensions

More terms from Don Reble, May 29 2003

a(32)-a(34) from Hugo Pfoertner, Nov 06 2019