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A164131
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Numbers k such that k^2 == 2 (mod 31).
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5
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8, 23, 39, 54, 70, 85, 101, 116, 132, 147, 163, 178, 194, 209, 225, 240, 256, 271, 287, 302, 318, 333, 349, 364, 380, 395, 411, 426, 442, 457, 473, 488, 504, 519, 535, 550, 566, 581, 597, 612, 628, 643, 659, 674, 690, 705, 721, 736, 752, 767, 783, 798, 814
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(n-1)+a(n-2)-a(n-3).
a(n) = (31+(-1)^(n-1)+62(n-1))/4.
G.f.: x*(8+15*x+8*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Aug 26 2009
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(15*Pi/62)*Pi/31. - Amiram Eldar, Feb 28 2023
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EXAMPLE
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At n= 4, a(4)=(31-1+186)/4=54. At n=5, a(5)=(31+1+248)/4=70.
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MATHEMATICA
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Select[Range[850], Mod[#^2, 31]==2&] (* Harvey P. Dale, Feb 04 2011 *)
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PROG
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(PARI) isok(k) = Mod(k, 31)^2 == 2; \\ Michel Marcus, Nov 22 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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