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A164135
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Numbers k such that k^2 == 2 (mod 47).
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5
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7, 40, 54, 87, 101, 134, 148, 181, 195, 228, 242, 275, 289, 322, 336, 369, 383, 416, 430, 463, 477, 510, 524, 557, 571, 604, 618, 651, 665, 698, 712, 745, 759, 792, 806, 839, 853, 886, 900, 933, 947, 980, 994, 1027, 1041, 1074, 1088, 1121, 1135, 1168, 1182
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OFFSET
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1,1
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COMMENTS
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Numbers congruent to {7, 40} mod 47. - Amiram Eldar, Feb 26 2023
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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) for n>3.
a(n) = (47+19*(-1)^n+94*(n-1))/4.
G.f.: x*(7+33*x+7*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Aug 26 2009
Sum_{n>=1} (-1)^(n+1)/a(n) = cot(7*Pi/47)*Pi/47. - Amiram Eldar, Feb 26 2023
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MAPLE
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MATHEMATICA
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Select[Range[2000], PowerMod[#, 2, 47]==2&] (* or *) LinearRecurrence[ {1, 1, -1}, {7, 40, 54}, 60] (* Harvey P. Dale, Sep 29 2013 *)
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PROG
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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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