A070424 a(n) = 7^n mod 41.

1, 7, 8, 15, 23, 38, 20, 17, 37, 13, 9, 22, 31, 12, 2, 14, 16, 30, 5, 35, 40, 34, 33, 26, 18, 3, 21, 24, 4, 28, 32, 19, 10, 29, 39, 27, 25, 11, 36, 6, 1, 7, 8, 15, 23, 38, 20, 17, 37, 13, 9, 22, 31, 12, 2, 14, 16, 30, 5, 35, 40, 34, 33, 26, 18, 3, 21, 24, 4, 28, 32, 19, 10, 29, 39

Offset

0,2

Comments

Sequence is periodic with length 40. Since a(20) = 40 (or -1), 41 is prime in Z[sqrt(7)]. - Alonso del Arte, Oct 11 2012

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

From R. J. Mathar, Apr 20 2010: (Start)

a(n) = a(n - 1) - a(n - 20) + a(n - 21).

G.f.: ( -1 -6*x -x^2 -7*x^3 -8*x^4 -15*x^5 +18*x^6 +3*x^7 -20*x^8 + 24*x^9 +4*x^10 -13*x^11 -9*x^12 +19*x^13 +10*x^14 -12*x^15 -2*x^16 - 14*x^17 +25*x^18 -30*x^19 -6*x^20 ) / ( (x - 1)*(x^4 + 1)*(x^16 -x^12 + x^8 -x^4 +1) ). (End)

a(n) = a(n-40). - G. C. Greubel, Mar 22 2016

Mathematica

PowerMod[7, Range[0, 74], 41] (* Alonso del Arte, Oct 12 2012 *)

Prog

(Sage) [power_mod(7, n, 41)for n in range(0, 75)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n)=lift(Mod(7, 41)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(7, n, 41): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Sequence in context: A047521 A231390 A231458 * A022097 A041100 A129658

Adjacent sequences: A070421 A070422 A070423 * A070425 A070426 A070427

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved