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 A159008 Positive numbers k such that k^2 == 2 (mod 89). 5
 25, 64, 114, 153, 203, 242, 292, 331, 381, 420, 470, 509, 559, 598, 648, 687, 737, 776, 826, 865, 915, 954, 1004, 1043, 1093, 1132, 1182, 1221, 1271, 1310, 1360, 1399, 1449, 1488, 1538, 1577, 1627, 1666, 1716, 1755, 1805, 1844, 1894, 1933, 1983, 2022, 2072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers congruent to {25, 64} mod 89. - Amiram Eldar, Feb 26 2023 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = a(n-1) + a(n-2) - a(n-3). G.f.: x*(25 + 39*x + 25*x^2)/((1+x)*(x-1)^2). a(n) = (89 + 11*(-1)^(n-1) + 178*(n-1))/4. Sum_{n>=1} (-1)^(n+1)/a(n) = tan(39*Pi/178)*Pi/89. - Amiram Eldar, Feb 26 2023 MATHEMATICA LinearRecurrence[{1, 1, -1}, {25, 64, 114}, 50] (* Vincenzo Librandi, Mar 02 2012 *) Select[Range[2100], PowerMod[#, 2, 89]==2&] (* Harvey P. Dale, May 09 2019 *) PROG (Magma) I:=[25, 64, 114]; [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 (PARI) for(n=1, 60, print1((89+11*(-1)^(n-1)+178*(n-1))/4", ")); \\ Vincenzo Librandi, Mar 02 2012 CROSSREFS Cf. A159007. Sequence in context: A211326 A103645 A061970 * A183373 A354381 A306358 Adjacent sequences: A159005 A159006 A159007 * A159009 A159010 A159011 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jun 30 2009 EXTENSIONS Slightly edited by R. J. Mathar, Jul 26 2009 STATUS approved

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Last modified August 3 23:57 EDT 2024. Contains 374905 sequences. (Running on oeis4.)