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A102710
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a(1) = 2, a(2) = 3, a(n+2) = a(n)*(a(n)+a(n+1)) - a(n+1).
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2, 3, 7, 23, 187, 4643, 898567, 4192705463, 3768229999719547, 15799096080675502645110083, 59534627833852486970959777827956950667527, 940593305274293766389990332525291876515204489479064901503485974103
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Every term is coprime to every other term.
The next term has 107 digits.
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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...
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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}] (* From Harvey P. Dale, Apr 23 2011 *)
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CROSSREFS
| Sequence in context: A111235 A066356 A006892 * A048824 A099073 A129724
Adjacent sequences: A102707 A102708 A102709 * A102711 A102712 A102713
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KEYWORD
| easy,nonn
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AUTHOR
| Leroy Quet Feb 05 2005
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EXTENSIONS
| More terms from Paul D. Hanna, Feb 05 2005
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