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A036122 a(n) = 2^n mod 29. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 21:25 EDT 2021. Contains 348155 sequences. (Running on oeis4.)