[seqfan] Re: sequence from a test

Artur grafix at csl.pl
Mon Dec 7 13:53:14 CET 2009

We can construct also few related sequences for fractional n

-15/8 * (3-sqrt(17))^(1/n)-15/8 * (3+sqrt(17))^
(1/n)+77/136 * (3+sqrt(17))^(1/n)
* sqrt(17)-77/136 * (3-sqrt(17))^(1/n)*sqrt(17)

a(n) = Degree of minimal polynomial for which

-15/8 * (3-sqrt(17))^(1/n)-15/8 * (3+sqrt(17))^
(1/n)+77/136 * (3+sqrt(17))^(1/n)
* sqrt(17)-77/136 * (3-sqrt(17))^(1/n)*sqrt(17)

is root

0,4, 6,16,25, (new for ONEIS)

8,124609,527758729,6283336319496262131908401,-145300841439648009494965894021269151109946912557
which will be coefficient by x^0 in polynomials for fractional n (after
changing in in formula n on 1/n)
etc.

n=1 polynomial of 0-degree  8
n=2 polynomial of 4-degree 124609+10008*x^2+272*x^4
n=3 polynomial of 6-degree
527758729-72502788*x+9960336*x^2-12497312*x^3+858432*x^4+73984*x^6
n=4 polynomial of 16-degree
6283336319496262131908401+69041316784325081240832*x^4
+307733115289100312576*x^8+570671352995905536*x^12+404961208827904*x^16
n=5 olynomial of 25-degree
-145300841439648009494965894021269151109946912557 -
200772711674665642426653097254178301375132160*x^5 -
100122948527964324789786143581423869624320*x^10 -
1507944984162000616677394937618104320*x^15 -
6487761036281393071333216092160*x^20 +
70931479522213353192685568*x^25

etc.

Is any from above interesting for ONEIS ?

Best wihes
Artur

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