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A152532
a(n) = prime(n) * prime(n+2) - 2 * prime(n+1).
5
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
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.
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
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 06 2008
STATUS
approved