A152532 a(n) = prime(n) * prime(n+2) - 2 * prime(n+1).

4, 11, 41, 69, 161, 213, 353, 505, 655, 1011, 1197, 1509, 1841, 2185, 2667, 3115, 3831, 4197, 4749, 5463, 5901, 6865, 7873, 8795, 9789, 10601, 11013, 11873, 13617, 14549, 17137, 17935, 20135, 20691, 23091, 24299, 25893, 27865

Offset

1,1

Comments

Before this sequence, a(24) = 8795 was an uninteresting number, see References and Links. For example: 8795 was mentioned in Sloane's Gap paper, pages 4-5: Which numbers do not appear in Sloane's encyclopedia? At the time of an initial calculation conducted in August 2008 by Philippe Guglielmetti, the smallest absent number tracked down was 8795.

References

Bartolo Luque, La brecha de Sloane: Tras la huella sociológica de las matemáticas, Investigación y Ciencia, Edición española de Scientific American, julio de 2014, p. 90-91.

Links

Table of n, a(n) for n=1..38.

Ingo Althofer, Is 8795 a boring number?

Nicolas Gauvrit, Jean-Paul Delahaye, Hector Zenil, Sloane's Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?, arXiv:1101.4470 [math.PR], p. 4-5.

Nicolas Gauvrit, Hector Zenil, Jean-Paul Delahaye, Le fossé de Sloane, Math. & Sci. hum. / Mathematics and Social Sciences,1413, n° 194, Summer 2011 (in French).

Charles R Greathouse IV, Uninteresting numbers.

Formula

a(n) = A000040(n)*A000040(n+2) - 2*A000040(n+1) = A090076(n) - A100484(n+1).

a(n) ~ n^2 log^2 n. - Charles R Greathouse IV, Sep 14 2015

Example

For n = 2, prime(2) = 3, prime(2+1) = 5 and prime(2+2) = 7, so a(2) = 3*7 - 2*5 = 21 - 10 = 11.
For n = 24, prime(24) = 89, prime(24+1) = 97 and prime(24+2) = 101, so a(24) = 89*101 - 2*97 = 8989 - 194 = 8795.

Maple

seq(ithprime(n)*ithprime(n+2)-2*ithprime(n+1), n=1..1000); # Robert Israel, Dec 21 2014

Mathematica

First[#]Last[#]-2#[[2]]&/@Partition[Prime[Range[100]], 3, 1] (* Harvey P. Dale, Jun 16 2011 *)

Prog

(PARI) a(n, p=prime(n))=my(q=nextprime(p+1)); p*nextprime(q+1) - 2*q
apply(p->a(0, p), primes(100)) \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A000040, A090076, A100484, A111071, A152527, A152528, A152529, A152530, A152531.

Sequence in context: A327025 A228190 A289283 * A343548 A121096 A047091

Adjacent sequences: A152529 A152530 A152531 * A152533 A152534 A152535

Keyword

easy,nonn

Author

Omar E. Pol, Dec 06 2008

Status

approved