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

Author

N. J. A. Sloane, May 05 2001

Keywords

• sign

Comments

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

References

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

Links

• 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)

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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

Python

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