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A114200
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When the n-th term of this sequence is added to or subtracted from the square of the n-th prime of the form 4k + 1 (i.e. A002144(n)), the result in both cases is a square.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
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EXAMPLE
| a(2) = 120 and A002144(2)=13. 13^2 - 120 = 7^2 and 13^2 + 120 = 17^2.
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CROSSREFS
| Cf. A002144.
Sequence in context: A126411 A137799 A198438 * A069074 A059775 A052762
Adjacent sequences: A114197 A114198 A114199 * A114201 A114202 A114203
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KEYWORD
| nonn
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AUTHOR
| Owen Mertens (owenmertens(AT)missouristate.edu), Nov 16 2005
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EXTENSIONS
| Definition corrected by Zak Seidov, Jul 20 2010
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