OFFSET
0,2
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 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,-1,1).
FORMULA
a(n) = a(n-1) - a(n-21) + a(n-22). - R. J. Mathar, Feb 08 2011
a(n) = a(n+42). - R. J. Mathar, Jun 04 2016
a(n) = 43 - a(n+21) for all n in Z. - Michael Somos, Oct 17 2018
MAPLE
i := pi(43) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[3, Range[0, 100], 43] (* G. C. Greubel, Oct 16 2018 *)
PadRight[{}, 120, {1, 3, 9, 27, 38, 28, 41, 37, 25, 32, 10, 30, 4, 12, 36, 22, 23, 26, 35, 19, 14, 42, 40, 34, 16, 5, 15, 2, 6, 18, 11, 33, 13, 39, 31, 7, 21, 20, 17, 8, 24, 29}] (* Harvey P. Dale, Mar 30 2019 *)
PROG
(PARI) a(n)=lift(Mod(3, 43)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 43): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..60], n->PowerMod(3, n, 43)); # Muniru A Asiru, Oct 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved