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A062116 a(n) = 2^n mod 17. 4
1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Period 8.

Terms of the simple continued fraction of 678982/(sqrt(10997122748477) - 2846611). - Paolo P. Lava, Aug 06 2009

REFERENCES

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).

FORMULA

a(n) = (1/56)*(73*(n mod 8) + 45*((n+1) mod 8) + 31*((n+2) mod 8) + 24*((n+3) mod 8) - 39*((n+4) mod 8) - 11*((n+5) mod 8) + 3*((n+6) mod 8) + 10*((n+7) mod 8)). - Paolo P. Lava, Nov 24 2006

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-1) - a(n-4) + a(n-5).

G.f.: (1 + x + 2*x^2 + 4*x^3 + 9*x^4)/((1-x)*(1+x^4)). (End)

a(n) = 17 - a(n+4) = a(n+8) for all n in Z. - Michael Somos, Oct 17 2018

EXAMPLE

a(5) = 32 mod 17 = 15.

MATHEMATICA

Mod[#, 17]&/@(2^Range[0, 100])  (* Harvey P. Dale, Mar 06 2011 *)

PROG

(PARI) { for (n=0, 1000, write("b062116.txt", n, " ", 2^n%17) ) } \\ Harry J. Smith, Aug 01 2009

(Sage) [power_mod(2, n, 17) for n in range(0, 87)] # Zerinvary Lajos, Nov 03 2009

(MAGMA) [2^n mod 17: n in [0..100]]; // G. C. Greubel, Oct 16 2018

(GAP) a:=List([0..70], n->PowerMod(2, n, 17));; Print(a); # Muniru A Asiru, Jan 29 2019

CROSSREFS

Cf. A036117, A036118.

Sequence in context: A309571 A210023 A301807 * A316749 A008381 A083780

Adjacent sequences:  A062113 A062114 A062115 * A062117 A062118 A062119

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Jun 06 2001

STATUS

approved

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Last modified January 27 05:41 EST 2021. Contains 340455 sequences. (Running on oeis4.)