A103845 Product of first n Lucas numbers, plus one.

1, 2, 4, 13, 85, 925, 16633, 482329, 22669417, 1722875617, 211913700769, 42170826452833, 13579006117811905, 7074662187380001985, 5963940223961341672513, 8134814465483270041306369

Offset: 0

Author

Jonathan Vos Post, Mar 30 2005

Keywords

• easy
• nonn

Comments

Prime for n = 1, 3, 6; semiprime for n = 2, 4, 7, 8, 9, 10, 13, 14, 15, 23, 26. a(n) asymptotic to Phi^A000217(n).

Examples

			a(10) = 1 * 3 * 4 * 7 * 11 * 18 * 29 * 47 * 76 * 123 + 1 = 211913700769 = 349 * 607202581 which is semiprime.
		

Crossrefs

Cf. A000045, A000204, A000217, A052449, A103815.

Programs

Mathematica

Join[{1},Rest[FoldList[Times,1,LucasL[Range[20]]]]+1] (* Harvey P. Dale, Oct 25 2011 *)

Formula

a(n) = Product[Lucasi[k], {k, 1, n}]+1. a(n) = Product[A000217(k), {k, 1, n}]+1.

a(n) = A070825(n)+1, n>0. - R. J. Mathar, Dec 22 2010