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A158803
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Numbers k such that k^2 == 2 (mod 41).
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6
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17, 24, 58, 65, 99, 106, 140, 147, 181, 188, 222, 229, 263, 270, 304, 311, 345, 352, 386, 393, 427, 434, 468, 475, 509, 516, 550, 557, 591, 598, 632, 639, 673, 680, 714, 721, 755, 762, 796, 803, 837, 844, 878, 885, 919, 926, 960, 967, 1001, 1008, 1042, 1049
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OFFSET
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1,1
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COMMENTS
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Numbers congruent to {17, 24} mod 41. - 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).
a(n) = (1/4)*(41 + 27*(-1)^(n-1) + 82*(n-1)).
First differences: a(2n) - a(2n-1) = 7, a(2n+1) - a(2n) = 34.
G.f.: x*(17 + 7*x + 17*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Apr 04 2009
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(7*Pi/82)*Pi/41. - Amiram Eldar, Feb 26 2023
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MATHEMATICA
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Select[Range[1200], PowerMod[#, 2, 41]==2&] (* Harvey P. Dale, Oct 24 2021 *)
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PROG
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(Magma) I:=[17, 24, 58]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Mar 02 2012
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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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Comments translated to formulas by R. J. Mathar, Apr 04 2009
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STATUS
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approved
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