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

Author

Omar E. Pol, Dec 06 2008

Keywords

• easy
• nonn

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.

Examples

			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.
		

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

• Ingo Althofer, Is 8795 a boring number?
• Nicolas Gauvrit, Jean-Paul Delahaye, and 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, and 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.

Crossrefs

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

Programs

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 *)

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

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