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

%I A152532 #54 May 30 2024 06:53:53
%S A152532 4,11,41,69,161,213,353,505,655,1011,1197,1509,1841,2185,2667,3115,
%T A152532 3831,4197,4749,5463,5901,6865,7873,8795,9789,10601,11013,11873,13617,
%U A152532 14549,17137,17935,20135,20691,23091,24299,25893,27865
%N A152532 a(n) = prime(n) * prime(n+2) - 2 * prime(n+1).
%C A152532 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.
%D A152532 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.
%H A152532 Ingo Althofer, <a href="http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=1&amp;topic=1830">Is 8795 a boring number?</a>
%H A152532 Nicolas Gauvrit, Jean-Paul Delahaye, and Hector Zenil, <a href="http://arxiv.org/abs/1101.4470">Sloane's Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?</a>, arXiv:1101.4470 [math.PR], p. 4-5.
%H A152532 Nicolas Gauvrit, Hector Zenil, and Jean-Paul Delahaye, <a href="https://www.cristal.univ-lille.fr/SMAC/publications/pdf/mss2011-fosse.pdf">Le fossé de Sloane</a>, Math. & Sci. hum. / Mathematics and Social Sciences,1413, n° 194, Summer 2011 (in French).
%H A152532 Charles R Greathouse IV, <a href="http://math.crg4.com/uninteresting.html">Uninteresting numbers</a>.
%F A152532 a(n) = A000040(n)*A000040(n+2) - 2*A000040(n+1) = A090076(n) - A100484(n+1).
%F A152532 a(n) ~ n^2 log^2 n. - _Charles R Greathouse IV_, Sep 14 2015
%e A152532 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.
%e A152532 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.
%p A152532 seq(ithprime(n)*ithprime(n+2)-2*ithprime(n+1), n=1..1000); # _Robert Israel_, Dec 21 2014
%t A152532 First[#]Last[#]-2#[[2]]&/@Partition[Prime[Range[100]],3,1] (* _Harvey P. Dale_, Jun 16 2011 *)
%o A152532 (PARI) a(n,p=prime(n))=my(q=nextprime(p+1)); p*nextprime(q+1) - 2*q
%o A152532 apply(p->a(0,p), primes(100)) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A152532 Cf. A000040, A090076, A100484, A111071, A152527, A152528, A152529, A152530, A152531.
%K A152532 easy,nonn
%O A152532 1,1
%A A152532 _Omar E. Pol_, Dec 06 2008