A112655 a(n) cubed is congruent to a(n) (mod 13).

0, 1, 12, 13, 14, 25, 26, 27, 38, 39, 40, 51, 52, 53, 64, 65, 66, 77, 78, 79, 90, 91, 92, 103, 104, 105, 116, 117, 118, 129, 130, 131, 142, 143, 144, 155, 156, 157, 168, 169, 170, 181, 182, 183, 194, 195, 196, 207, 208, 209, 220, 221, 222, 233, 234, 235, 246

Offset

0,3

Comments

Numbers k such that k == -1, 0, or 1 (mod 13). - Chai Wah Wu, May 27 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

From Chai Wah Wu, May 27 2025: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3.

G.f.: x*(x^2 + 11*x + 1)/(x^4 - x^3 - x + 1). (End)

Example

a(3) = 13 because 13^3 = 2197 = 0 (mod 13) and 13 = 0 (mod 13)

Maple

m = 13 for n = 1 to 300 if n^3 mod m = n mod m then print n; next n

Mathematica

Select[Range[0, 250], Mod[#, 13]==PowerMod[#, 3, 13]&] (* Harvey P. Dale, Oct 09 2023 *)

Prog

(Python)
def A112655(n):
    a, b = divmod(n, 3)
    return (0, 1, 12)[b]+a*13 # Chai Wah Wu, May 27 2025

Crossrefs

Cf. A070475.

Sequence in context: A045879 A257073 A239722 * A308919 A048026 A115662

Adjacent sequences: A112652 A112653 A112654 * A112656 A112657 A112658

Keyword

easy,nonn

Author

Jeremy Gardiner, Dec 28 2005

Status

approved