A066266 Product of first n primorials + 1.

3, 13, 361, 75601, 174636001, 5244319080001, 2677277333530800001, 25968760179275365452000001, 5793445238736255798985527240000001, 37481813439427687898244906452608585200000001, 7517370874372838151564668004911177464757864076000000001

Offset

1,1

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.

Formula

a(n) = A006939(n) + 1. - Andrew Howroyd, Dec 10 2024

Example

a(3)=361 since 361 = (2)*(2*3)*(2*3*5) + 1.

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 *)

Prog

(PARI) a(n) = 1 + prod(k=1, n, prime(k)^(n-k+1)) \\ Andrew Howroyd, Dec 10 2024

Crossrefs

Cf. A066267, A066268, A066269, A002110, A006939, A005234.

Sequence in context: A180654 A260576 A156358 * A092845 A216474 A222762

Adjacent sequences: A066263 A066264 A066265 * A066267 A066268 A066269

Keyword

nonn

Author

Patrick De Geest, Dec 16 2001

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 08 2010

Status

approved