id:A102710 - OEIS Search Results

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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; listen)

	OFFSET	`1,1`
	COMMENT	`Every term is coprime to every other term.` `The next term has 107 digits.`
	LINKS	`Leroy Quet, Home Page (listed in lieu of email address)`
	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...`
	CROSSREFS	`Sequence in context: A111235 A066356 A006892 this_sequence A048824 A099073 A129724` `Adjacent sequences: A102707 A102708 A102709 this_sequence A102711 A102712 A102713`
	KEYWORD	`easy,nonn`
	AUTHOR	`Leroy Quet Feb 05 2005`
	EXTENSIONS	`More terms from Paul D. Hanna, Feb 05 2005`

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

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