A036122 a(n) = 2^n mod 29.

1, 2, 4, 8, 16, 3, 6, 12, 24, 19, 9, 18, 7, 14, 28, 27, 25, 21, 13, 26, 23, 17, 5, 10, 20, 11, 22, 15, 1, 2, 4, 8, 16, 3, 6, 12, 24, 19, 9, 18, 7, 14, 28, 27, 25, 21, 13, 26, 23, 17, 5, 10, 20, 11, 22, 15, 1, 2, 4, 8, 16, 3

Offset

0,2

Comments

The sequence is 28-periodic.

References

I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = a(n-1) - a(n-14) + a(n-15). - R. J. Mathar, Feb 06 2011

G.f.: (-1 - x - 2*x^2 - 4*x^3 - 8*x^4 + 13*x^5 - 3*x^6 - 6*x^7 - 12*x^8 + 5*x^9 + 10*x^10 - 9*x^11 + 11*x^12 - 7*x^13 - 15*x^14) / ((x-1)*(x^2+1)*(x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1)). - R. J. Mathar, Feb 06 2011

a(n) = a(n+28). - R. J. Mathar, Jun 04 2016

a(n) = 29 - a(n+14) for all n in Z. - Michael Somos, Oct 17 2018

Maple

i := pi(29) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];

Mathematica

PowerMod[2, Range[0, 70], 29] (* Harvey P. Dale, Mar 26 2012 *)

Prog

(Sage) [power_mod(2, n, 29) for n in range(0, 62)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=lift(Mod(2, 29)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 29): n in [0..100]]; // G. C. Greubel, Oct 16 2018
(GAP) List([0..65], n->PowerMod(2, n, 29)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000079 (2^n).

Sequence in context: A218338 A218468 A308539 * A050124 A101943 A331440

Adjacent sequences: A036119 A036120 A036121 * A036123 A036124 A036125

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved