A120384 Isolated primes: geometric mean of distances of a prime to neighboring primes sets record.

3, 5, 7, 23, 53, 89, 113, 211, 1259, 1327, 1847, 2179, 2503, 5623, 14107, 19661, 24281, 38501, 58831, 268343, 396833, 1272749, 2198981, 3863107, 4411963, 4958131, 5102953, 7950001, 8917523, 10938023, 12623189, 22440841, 24662467, 32616223

Offset: 1

Author

Alexis Monnerot-Dumaine, Jun 29 2006

Keywords

• nonn

Comments

A096265 is based on arithmetic mean or total distance to neighbors. But it doesn't say if it is isolated from them or close to one of them.

Examples

			a(4) = 23 because the distance (geometric mean) to its neighbors (19 and 29) equals = sqrt(4*6) = 4.8989. No smaller prime is more isolated. The next more isolated prime a(5) is 53.
		

Links

• Ken Takusagawa, Table of n, a(n) for n = 1..54

Crossrefs

Cf. A096265.

Programs

PARI

lista(nn) = {d = 0; p = 1; q = 2; r = 3; for (i=1, nn, p = q; q = r; r = nextprime(r+1); if ((nd = (q-p)*(r-q)) > d, print1(q, ", "); d = nd;););} \\ Michel Marcus, Jun 12 2013

Extensions

Offset corrected and a(22)-a(34) added by Donovan Johnson, May 23 2010