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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
OFFSET
0,2
COMMENTS
The sequence is 28-periodic.
REFERENCES
I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
LINKS
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 A378106
KEYWORD
nonn,easy
STATUS
approved