OFFSET
0,1
COMMENTS
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
All numbers in the range [primorial(n)+2, a(n)-1] are guaranteed to be a multiple of a prime p whose index is <= n. There are prime(n+1)-2 = A040976(n+1) such numbers. - Jamie Morken and Michel Marcus, Feb 01 2018
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..100
Hisanori Mishima, WIFC (World Integer Factorization Center): PI Pn + NextPrime (n = 1 to 100), PI Pn - NextPrime (n = 1 to 100), PI Pn + 1 (n = 1 to 100), PI Pn - 1 (n = 1 to 100).
Eric Weisstein's World of Mathematics, Prime Gaps
FORMULA
EXAMPLE
a(2) = 2*3 + 5 = 11.
MAPLE
a:= n-> mul(ithprime(k), k=1..n)+ithprime(n+1): seq(a(n), n=0..20); # Muniru A Asiru, Feb 01 2018
MATHEMATICA
Module[{nn=20, pr}, pr=Prime[Range[nn+1]]; Join[{3}, FoldList[ Times, Most[ pr]] + Rest[pr]]] (* Harvey P. Dale, Feb 19 2016 *)
Total /@ Fold[Append[#1, {Prime[#2] #1[[-1, 1]], Prime[#2 + 1]}] &, {{1, 2}}, Range@ 17] (* Michael De Vlieger, Feb 21 2018 *)
PROG
(PARI) { n=-1; m=1; forprime (p=2, prime(101), write("b060881.txt", n++, " ", m + p); m*=p; ) } \\ Harry J. Smith, Jul 19 2009
(PARI) a(n) = prod(i=1, n, prime(i)) + prime(n+1); \\ Michel Marcus, Feb 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 05 2001
EXTENSIONS
Name changed by David A. Corneth, Mar 25 2018
STATUS
approved