A152527 -id:A152527 - cp's OEIS frontend

A111071 Difference between the product of two consecutive primes and the next prime.

1, 8, 24, 64, 126, 202, 300, 408, 636, 862, 1106, 1474, 1716, 1968, 2432, 3066, 3532, 4016, 4684, 5104, 5684, 6468, 7290, 8532, 9694, 10296, 10912, 11550, 12190, 14220, 16500, 17808, 18894, 20560, 22342, 23544, 25424, 27048, 28712, 30786, 32208

Offset: 1

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 09 2005

nonn

			a(4)= prime(4)*prime(5)-prime(6) = 7*11-13=64.

Cf. A000040.

[NthPrime(n)*NthPrime(n+1)-NthPrime(n+2): n in [1..50]]; // Vincenzo Librandi, Jul 18 2015

seq(ithprime(n)*ithprime(n+1)-ithprime(n+2), n=1..50); # Emeric Deutsch, Oct 10 2005

f[n_] := Prime[n]Prime[n + 1] - Prime[n + 2]; Table[ f[n], {n, 41}] (* Robert G. Wilson v, Oct 10 2005  *)
#[[1]]*#[[2]]-#[[3]]&/@Partition[Prime[Range[50]],3,1] (* Harvey P. Dale, Aug 06 2015 *)

main(size)=my(n);vector(size,n,prime(n)*prime(n+1)-prime(n+2)) /* Anders Hellström, Jul 16 2015 */

a(n) = prime(n)*prime(n+1)-prime(n+2) = A006094(n)-A000040(n+2) = 2*A152527(n-1).

More terms from Robert G. Wilson v and Emeric Deutsch, Oct 10 2005

A152528 a(n) = p(n)p(n+2) - 3p(n+1), where p(n) is the n-th prime.

Original entry on oeis.org

1, 6, 34, 58, 148, 196, 334, 482, 626, 980, 1160, 1468, 1798, 2138, 2614, 3056, 3770, 4130, 4678, 5390, 5822, 6782, 7784, 8698, 9688, 10498, 10906, 11764, 13504, 14422, 17006, 17798, 19996, 20542, 22940, 24142, 25730, 27698

Offset: 1

Omar E. Pol, Dec 06 2008

Cf. A000040, A111071, A152527, A152529, A152530, A152531, A152532.

A152528 := proc(n)
    ithprime(n)*ithprime(n+2)-3*ithprime(n+1) ;
end proc: # R. J. Mathar, Jul 28 2015

#[[1]]*#[[3]]-3*#[[2]]&/@Partition[Prime[Range[50]],3,1] (* Harvey P. Dale, Jul 14 2014 *)

A152529 a(n) = (p(n)p(n+2) - 3p(n+1))/2, where p(n) is the n-th odd prime.

Original entry on oeis.org

3, 17, 29, 74, 98, 167, 241, 313, 490, 580, 734, 899, 1069, 1307, 1528, 1885, 2065, 2339, 2695, 2911, 3391, 3892, 4349, 4844, 5249, 5453, 5882, 6752, 7211, 8503, 8899, 9998, 10271, 11470, 12071, 12865, 13849, 14687, 15388, 16823

Offset: 1

Omar E. Pol, Dec 06 2008

Cf. A065091, A111071, A152527, A152528, A152530, A152531, A152532.

A152529 := proc(n)
    j := n+1 ;
    ithprime(j)*ithprime(j+2)-3*ithprime(j+1) ;
    %/2 ;
end proc: # R. J. Mathar, Jul 28 2015

a(n) = A152528(n+1)/2.

A152530 a(n) = p(n)*p(n+2)-p(n+1), where p(n) is the n-th prime.

Original entry on oeis.org

7, 16, 48, 80, 174, 230, 372, 528, 684, 1042, 1234, 1550, 1884, 2232, 2720, 3174, 3892, 4264, 4820, 5536, 5980, 6948, 7962, 8892, 9890, 10704, 11120, 11982, 13730, 14676, 17268, 18072, 20274, 20840, 23242, 24456, 26056, 28032

Offset: 1

Omar E. Pol, Dec 06 2008

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A111071, A152527, A152528, A152529, A152531, A152532.

A152530 := proc(n)
    ithprime(n)*ithprime(n+2)-ithprime(n+1) ;
end proc: # R. J. Mathar, Jul 28 2015

#[[1]]#[[3]]-#[[2]]&/@Partition[Prime[Range[50]],3,1] (* Harvey P. Dale, Dec 19 2012 *)

A152531 a(n) = (p(n)*p(n+2) - p(n+1))/2, where p(n) is the n-th odd prime.

Original entry on oeis.org

8, 24, 40, 87, 115, 186, 264, 342, 521, 617, 775, 942, 1116, 1360, 1587, 1946, 2132, 2410, 2768, 2990, 3474, 3981, 4446, 4945, 5352, 5560, 5991, 6865, 7338, 8634, 9036, 10137, 10420, 11621, 12228, 13028, 14016, 14860, 15567, 17004

Offset: 1

Omar E. Pol, Dec 06 2008

This is A111071 without its first term. - R. J. Mathar, Jul 27 2015

Cf. A065091, A111071, A152527, A152528, A152529, A152530, A152532.

A152531 := proc(n)
    j := n+1 ;
    ithprime(j)*ithprime(j+2)-ithprime(j+1) ;
    %/2 ;
end proc: # R. J. Mathar, Jul 28 2015

(First[#]*Last[#]-#[[2]])/2&/@Partition[Prime[Range[2,50]],3,1] (* Harvey P. Dale, Oct 09 2014 *)

a(n) = A152530(n+1)/2.

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

Original entry on oeis.org

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

Omar E. Pol, Dec 06 2008

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.

			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.

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.

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.

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

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

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

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

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

cp's OEIS Frontend

A111071 Difference between the product of two consecutive primes and the next prime.

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A152528 a(n) = p(n)*p(n+2) - 3*p(n+1), where p(n) is the n-th prime.

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A152529 a(n) = (p(n)*p(n+2) - 3*p(n+1))/2, where p(n) is the n-th odd prime.

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A152530 a(n) = p(n)*p(n+2)-p(n+1), where p(n) is the n-th prime.

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A152531 a(n) = (p(n)*p(n+2) - p(n+1))/2, where p(n) is the n-th odd prime.

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

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Maple

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Formula

A152528 a(n) = p(n)p(n+2) - 3p(n+1), where p(n) is the n-th prime.

A152529 a(n) = (p(n)p(n+2) - 3p(n+1))/2, where p(n) is the n-th odd prime.