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

1,1

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A096265.

Sequence in context: A038916 A019363 A288890 * A216124 A096505 A214680

Adjacent sequences: A120381 A120382 A120383 * A120385 A120386 A120387

Keyword

nonn

Author

Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Jun 29 2006

Extensions

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

Status

approved