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
KEYWORD
sign
AUTHOR
N. J. A. Sloane, May 05 2001
STATUS
approved