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A036136 a(n) = 3^n mod 89. 3
1, 3, 9, 27, 81, 65, 17, 51, 64, 14, 42, 37, 22, 66, 20, 60, 2, 6, 18, 54, 73, 41, 34, 13, 39, 28, 84, 74, 44, 43, 40, 31, 4, 12, 36, 19, 57, 82, 68, 26, 78, 56, 79, 59, 88, 86, 80, 62, 8, 24, 72, 38, 25, 75, 47, 52, 67, 23 (list; graph; refs; listen; history; text; internal format)
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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

FORMULA

From G. C. Greubel, Oct 17 2018: (Start)

a(n) = a(n-1) - a(n-44) + a(n-45).

a(n+88) = a(n). (End)

MAPLE

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

MATHEMATICA

PowerMod[3, Range[0, 100], 89] (* G. C. Greubel, Oct 17 2018 *)

PROG

(PARI) a(n)=lift(Mod(3, 89)^n) \\ Charles R Greathouse IV, Mar 22 2016

(MAGMA) [Modexp(3, n, 89): n in [0..100]]; // G. C. Greubel, Oct 17 2018

(Python) for n in range(0, 100): print(int(pow(3, n, 89)), end=' ') # Stefano Spezia, Oct 17 2018

(GAP) List([0..60], n->PowerMod(3, n, 89)); # Muniru A Asiru, Oct 17 2018

CROSSREFS

Cf. A000244 (3^n).

Sequence in context: A329023 A001218 A036158 * A271350 A057262 A057232

Adjacent sequences:  A036133 A036134 A036135 * A036137 A036138 A036139

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 27 13:13 EDT 2020. Contains 337380 sequences. (Running on oeis4.)