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 A156638 Numbers k such that k^2 + 2 == 0 (mod 9). 8
 4, 5, 13, 14, 22, 23, 31, 32, 40, 41, 49, 50, 58, 59, 67, 68, 76, 77, 85, 86, 94, 95, 103, 104, 112, 113, 121, 122, 130, 131, 139, 140, 148, 149, 157, 158, 166, 167, 175, 176, 184, 185, 193, 194, 202, 203, 211, 212, 220, 221, 229, 230, 238, 239, 247, 248, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Artur Jasinski, Apr 30 2010: (Start) Numbers congruent to 4 or 5 mod 9. Numbers which are not the sum of 3 cubes. Complement to A060464. (End) Numbers k such that A010888(k^2) = 7. - V.J. Pohjola, Aug 18 2012 REFERENCES Henri Cohen, Number Theory Volume I: Tools and Diophantine Equations. Springer Verlag (2007) p. 380. - Artur Jasinski, Apr 30 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Andrew Sutherland, Sums of three cubes, Slides of a talk given May 07 2020 on the Number Theory Web. Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA For n > 2, a(n) = a(n-2) + 9. G.f.: x*(4*x^2 + x + 4)/(x^3 - x^2 - x + 1). - Alexander R. Povolotsky, Feb 15 2009 From R. J. Mathar, Feb 19 2009: (Start) a(n) = a(n-1) + a(n-2) - a(n-3), n>3. a(n) = 9*n/2 - 9/4 - 7*(-1)^n/4. G.f.: x*(4 + x + 4*x^2)/((1 + x)*(1 - x)^2). (End) a(n) = -a(-n+1). - Bruno Berselli, Jan 08 2012 E.g.f.: 4 + ((18*x - 9)*exp(x) - 7*exp(-x))/4. - David Lovler, Aug 21 2022 Sum_{n>=1} (-1)^(n+1)/a(n) = tan(Pi/18)*Pi/9. - Amiram Eldar, Sep 26 2022 MAPLE A156638:=n->9*n/2 - 9/4 - 7*(-1)^n/4: seq(A156638(n), n=1..80); # Wesley Ivan Hurt, Aug 16 2015 MATHEMATICA LinearRecurrence[{1, 1, -1}, {4, 5, 13}, 50] (* Vincenzo Librandi, Mar 01 2012 *) Flatten[Table[9n - {5, 4}, {n, 30}]] (* Alonso del Arte, Aug 09 2015 *) Select[Range[300], PowerMod[#, 2, 9]==7&] (* Harvey P. Dale, Jan 31 2023 *) PROG (Magma) [9*n/2 - 9/4 - 7*(-1)^n/4 : n in [1..80]]; // Wesley Ivan Hurt, Aug 16 2015 (PARI) a(n) = (18*n - 9 - 7*(-1)^n)/4 \\ David Lovler, Aug 21 2022 CROSSREFS Cf. A060464, A010888, A334521, A334522. Sequence in context: A283483 A288755 A227897 * A098868 A087882 A338544 Adjacent sequences: A156635 A156636 A156637 * A156639 A156640 A156641 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Feb 12 2009 STATUS approved

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Last modified December 2 08:12 EST 2023. Contains 367515 sequences. (Running on oeis4.)