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A120384
Isolated primes: geometric mean of distances of a prime to neighboring primes sets record.
1
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
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
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