A102710 a(1) = 2, a(2) = 3, a(n+2) = a(n)*(a(n)+a(n+1)) - a(n+1).

2, 3, 7, 23, 187, 4643, 898567, 4192705463, 3768229999719547, 15799096080675502645110083, 59534627833852486970959777827956950667527, 940593305274293766389990332525291876515204489479064901503485974103

Offset

1,1

Comments

Every term is coprime to every other term.

The next term has 107 digits.

Links

Table of n, a(n) for n=1..12.

Formula

a(n+2) = -a(n+1) + 5*product{k=1 to n} a(k)

Comments on asymptotics from Paul D. Hanna, Feb 05 2005:

Limit_{n->inf} log(a(n+1))/log(a(n)) = (sqrt(5)+1)/2 = 1.6180339887...

Limit_{n->inf} log(a(n))/((sqrt(5)+1)/2)^n = 0.471775871...

Limit_{n->inf} fraction( a(2n+2)/a(2n+1) ) = 0.9963258537736462872363456738414777019251922501451462595067...

Limit_{n->inf} fraction( a(2n+1)/a(2n) ) = 0.5781727423883458291832179527899399497969420087427440931499...

Mathematica

RecurrenceTable[{a[1]==2, a[2]==3, a[n]==a[n-2](a[n-2]+a[n-1])- a[n-1]}, a, {n, 12}]  (* Harvey P. Dale, Apr 23 2011 *)

Crossrefs

Sequence in context: A066356 A006892 A296397 * A048824 A355015 A099073

Adjacent sequences: A102707 A102708 A102709 * A102711 A102712 A102713

Keyword

easy,nonn

Author

Leroy Quet, Feb 05 2005

Extensions

More terms from Paul D. Hanna, Feb 05 2005

Status

approved