A060881 n-th primorial (A002110) + prime(n + 1).

3, 5, 11, 37, 221, 2323, 30047, 510529, 9699713, 223092899, 6469693261, 200560490167, 7420738134851, 304250263527253, 13082761331670077, 614889782588491463, 32589158477190044789, 1922760350154212639131

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn

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

Examples

			a(2) = 2*3 + 5 = 11.
		

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

Crossrefs

Cf. A000040, A002110, A060882, A006862, A057588.

Programs

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 *)

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

Formula

a(n) = A002110(n) + A000040(n+1). - Michel Marcus, Feb 01 2018

Extensions

Name changed by David A. Corneth, Mar 25 2018