id:A114200 - OEIS Search Results

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When the n-th term of this sequence is added to or subtracted from the n-th prime of the form 4k + 1 (i.e. A002144(n)), the result in both cases is a square.

+0
2

24, 120, 240, 840, 840, 720, 2520, 1320, 5280, 6240, 9360, 3960, 10920, 3360, 18480, 14280, 24400, 17160, 6840, 31920, 10920, 26520, 43680, 50160, 16320, 35880, 57960, 73920, 38760, 15600, 46200, 100800, 107640, 122400, 138600, 128520, 148200 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`This sequence and A002144 give rise to a class of monic polynomials x^2 + bx + c where b = +/-A002144(n) and c = +/-a(n)/4 that will factor over the integers regardless of the sign of c. For example, x^2 - 13x - 30 and x^2 - 13x + 30 are two such polynomials. Further polynomials with this property can be found by transforming the roots.`
	EXAMPLE	`a(2) = 120 and A002144(2)=13. 13^2 - 120 = 7^2 and 13^2 + 120 = 17^2.`
	CROSSREFS	`Cf. A002144.` `Sequence in context: A124952 A126411 A137799 this_sequence A069074 A059775 A052762` `Adjacent sequences: A114197 A114198 A114199 this_sequence A114201 A114202 A114203`
	KEYWORD	`nonn`
	AUTHOR	`Owen Mertens (owenmertens(AT)missouristate.edu), Nov 16 2005`

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Last modified December 11 12:57 EST 2009. Contains 170656 sequences.

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