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

0,4

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)

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A058193 A065314 A065316 * A367182 A221670 A128334

Adjacent sequences: A060879 A060880 A060881 * A060883 A060884 A060885

Keyword

sign

Author

N. J. A. Sloane, May 05 2001

Status

approved