A066266 Product of first n primorials + 1.
3, 13, 361, 75601, 174636001, 5244319080001, 2677277333530800001, 25968760179275365452000001, 5793445238736255798985527240000001, 37481813439427687898244906452608585200000001, 7517370874372838151564668004911177464757864076000000001
Offset: 1
Keywords
Examples
a(3)=361 since 361 = (2)*(2*3)*(2*3*5) + 1.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..37
- Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From N. J. A. Sloane, Jun 13 2012
- Carlos Rivera, Puzzle 118. Primorial product numbers, The Prime Puzzles & Problems Connection.
- Eric Weisstein's World of Mathematics, Primorial.
Programs
-
Mathematica
Table[Times@@Table[Times@@Prime[Range[n]],{n,k}]+1,{k,40}] (* Jayanta Basu, May 12 2013 *) Rest[FoldList[Times,1,Rest[FoldList[Times,1,Prime[Range[10]]]]]]+1 (* Harvey P. Dale, Sep 16 2013 *) -
PARI
a(n) = 1 + prod(k=1, n, prime(k)^(n-k+1)) \\ Andrew Howroyd, Dec 10 2024
Formula
a(n) = A006939(n) + 1. - Andrew Howroyd, Dec 10 2024
Extensions
Offset changed from 0 to 1 by Harry J. Smith, Feb 08 2010