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A036137 a(n) = 5^n mod 97. 3
1, 5, 25, 28, 43, 21, 8, 40, 6, 30, 53, 71, 64, 29, 48, 46, 36, 83, 27, 38, 93, 77, 94, 82, 22, 13, 65, 34, 73, 74, 79, 7, 35, 78, 2, 10, 50, 56, 86, 42, 16, 80, 12, 60, 9, 45, 31, 58, 96, 92, 72, 69, 54, 76, 89, 57, 91, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

FORMULA

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

a(n) = a(n-1) - a(n-48) + a(n-49).

a(n+96) = a(n). (End)

EXAMPLE

As 5^5 = 3125 = k * 97 + 21 for some k and 0 <= 21 < 97, a(5) = 21. - David A. Corneth, Oct 17 2018

MAPLE

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

MATHEMATICA

PowerMod[5, Range[0, 100], 97] (* G. C. Greubel, Oct 17 2018 *)

PROG

(PARI) a(n)=lift(Mod(5, 97)^n) \\ Charles R Greathouse IV, Mar 22 2016

(Python) for n in range(0, 100): print(int(pow(5, n, 97)), end=' ') # Stefano Spezia, Oct 17 2018

(GAP) List([0..60], n->PowerMod(5, n, 97)); # Muniru A Asiru, Oct 17 2018

(MAGMA) [Modexp(5, n, 97): n in [0..100]]; // G. C. Greubel, Oct 18 2018

CROSSREFS

Cf. A000351 (5^n).

Sequence in context: A136912 A137111 A137110 * A070380 A068574 A000350

Adjacent sequences:  A036134 A036135 A036136 * A036138 A036139 A036140

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)