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A036131 a(n) = 2^n mod 67. 4
1, 2, 4, 8, 16, 32, 64, 61, 55, 43, 19, 38, 9, 18, 36, 5, 10, 20, 40, 13, 26, 52, 37, 7, 14, 28, 56, 45, 23, 46, 25, 50, 33, 66, 65, 63, 59, 51, 35, 3, 6, 12, 24, 48, 29, 58, 49, 31, 62, 57, 47, 27, 54, 41, 15, 30, 60, 53 (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,-1,1).

FORMULA

a(n) = a(n+66). - R. J. Mathar, Jun 04 2016

a(n) = a(n-1) - a(n-33) + a(n-34). - G. C. Greubel, Oct 17 2018

EXAMPLE

As 2^10 = 1024 = 67 * k + 19 for some k and 0 <= 19 < 67, a(10) = 19. - David A. Corneth, Oct 17 2018

MAPLE

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

MATHEMATICA

PowerMod[2, Range[0, 100], 67] (* G. C. Greubel, Oct 17 2018 *)

PROG

(PARI) a(n)=lift(Mod(2, 67)^n) \\ Charles R Greathouse IV, Mar 22 2016

(MAGMA) [Modexp(2, n, 67): n in [0..100]]; // G. C. Greubel, Oct 17 2018

(Python) for n in range(0, 100): print(int(pow(2, n, 67)), end=' ') # Stefano Spezia, Oct 17 2018

(GAP) List([0..60], n->PowerMod(2, n, 67)); # Muniru A Asiru, Oct 17 2018

CROSSREFS

Cf. A000079 (2^n).

Sequence in context: A036138 A000855 A036135 * A115424 A225878 A323097

Adjacent sequences:  A036128 A036129 A036130 * A036132 A036133 A036134

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)