A060881 -id:A060881 - cp's OEIS frontend

A060882 a(n) = n-th primorial (A002110) minus next prime.

-1, -1, 1, 23, 199, 2297, 30013, 510491, 9699667, 223092841, 6469693199, 200560490093, 7420738134769, 304250263527167, 13082761331669983, 614889782588491357, 32589158477190044671, 1922760350154212639009

Offset: 0

N. J. A. Sloane, May 05 2001

sign

It is well-known and easy to prove (see Honsbeger) that a(n) > 0 for n > 1. - N. J. A. Sloane, Jul 05 2009

Terms are pairwise coprime with very high probability. I didn't find terms which are pairwise noncoprime, although it may be a case of the "strong law of small numbers." - Daniel Forgues, Apr 23 2012

R. Honsberger, Mathematical Diamonds, MAA, 2003, see p. 79. [Added by N. J. A. Sloane, Jul 05 2009]

Harry J. Smith, Table of n, a(n) for n = 0..100
Hisanori Mishima, P1 * Pn + NextPrime (n = 1 to 100)
Hisanori Mishima, P1 * Pn - NextPrime (n = 1 to 100)
Hisanori Mishima, P1 * Pn + 1 (n = 1 to 100)
Hisanori Mishima, P1 * Pn - 1 (n = 1 to 100)
Hisanori Mishima, WIFC (World Integer Factorization Center)

Cf. A002110, A060881, A064819, A006862, A057588.

pp:=n->mul(ithprime(i),i=1..n);
[seq(pp(n)-ithprime(n+1),n=1..20)];

Join[{-1},With[{nn=20},#[[1]]-#[[2]]&/@Thread[{FoldList[Times,1, Prime[ Range[nn]]],Prime[Range[nn+1]]}]]] (* Harvey P. Dale, May 10 2013 *)

{ n=-1; m=1; forprime (p=2, prime(101), write("b060882.txt", n++, " ", m - p); m*=p; ) } \\ Harry J. Smith, Jul 13 2009

from sympy import prime, primorial
def A060882(n): return primorial(n)-prime(n+1) if n else -1 # Chai Wah Wu, Feb 25 2023

A065315 Smallest prime divisor of n-th primorial + (n+1)-st prime.

Original entry on oeis.org

5, 11, 37, 13, 23, 30047, 510529, 9699713, 127, 107, 433, 1093, 375569, 13082761331670077, 941879, 32589158477190044789, 1922760350154212639131, 4129, 92388407, 5879, 40729680599249024150621323549, 1783, 4903, 10279098043, 191, 131, 109, 163, 337, 20261, 673327, 6599, 181

Offset: 1

Labos Elemer, Oct 29 2001

nonn

			For n=3, 3rd primorial=30, prime(4)=7, sum=37, so a(3)=37.

Tyler Busby, Table of n, a(n) for n = 1..84 (terms 1..79 from Sean A. Irvine)
Romeo Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012-2023. - From N. J. A. Sloane, Jun 13 2012

Cf. A002110, A000040, A006530, A057713, A002584, A002585, A051342, A060881.

A065317 Largest prime divisor of the sum of the n-th primorial and the (n+1)-st prime.

Original entry on oeis.org

5, 11, 37, 17, 101, 30047, 510529, 9699713, 1427, 76829, 789077, 659863, 810104837, 13082761331670077, 652833094897, 32589158477190044789, 1922760350154212639131, 28406001782370300553, 770555057, 94904036422299534098897, 40729680599249024150621323549

Offset: 1

Labos Elemer, Oct 29 2001

nonn

			For n = 4, 4th primorial = 210, prime(5) = 11, sum = 210 + 11 = 13 * 17, a(4) = 17.

Tyler Busby, Table of n, a(n) for n = 1..84 (terms 1..68 from Daniel Suteu, terms 69..79 from Sean A. Irvine)
Romeo Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From _N. J. A. Sloane_, Jun 13 2012

Cf. A002110, A000040, A060881, A006530, A057713, A002584, A002585, A051342.

cp's OEIS Frontend

A060882 a(n) = n-th primorial (A002110) minus next prime.

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A065315 Smallest prime divisor of n-th primorial + (n+1)-st prime.

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A065317 Largest prime divisor of the sum of the n-th primorial and the (n+1)-st prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions