A156638 Numbers k such that k^2 + 2 == 0 (mod 9).

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

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