A147525 - OEIS

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A147525

Numbers X such that there exists Y in N : X^2=309*Y^2+103

1818362, 233487592671260018, 29981079637522561422843699458, 3849734052023190225799987829591837303402, 494326837141597862882377389715613614004616427568522 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`obtained with the fundamental unit 64202725495+3652365444*\sqrt(309) of Q(sqrt(309))`
	FORMULA	`a(n+2)=128405450990a(n+1)-a(n);` `a(n)=909181{[64202725495+3652365444sqrt(309)]^n+[64202725495-3652365444sqrt(309)]^n}-(103443/2){[64202725495-3652365444 sqrt(309)]^nsqrt(309)-[64202725495+3652365444sqrt(309)]^n*sqrt(309)}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 25 2008]`
	EXAMPLE	`a(1)=1818362 because the first relation is : 1818362^2=309*103443^2+103`
	CROSSREFS	`Sequence in context: A137819 A145537 A183735 * A205412 A204951 A205639` `Adjacent sequences: A147522 A147523 A147524 * A147526 A147527 A147528`
	KEYWORD	`easy,nonn`
	AUTHOR	`Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 06 2008`

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Last modified February 17 02:31 EST 2012. Contains 205978 sequences.