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A088227 Solutions x to x^n == 7 mod 13. 1
2, 6, 7, 11, 15, 19, 20, 24, 28, 32, 33, 37, 41, 45, 46, 50, 54, 58, 59, 63, 67, 71, 72, 76, 80, 84, 85, 89, 93, 97, 98, 102, 106, 110, 111, 115, 119, 123, 124, 128, 132, 136, 137, 141, 145, 149, 150, 154, 158, 162, 163, 167, 171, 175, 176, 180, 184, 188, 189, 193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primitive roots of 13. The first differences are periodic: 4,1,4,4,4,1,4,4,4,1,4,4,... - Paolo P. Lava, Feb 29 2008

REFERENCES

E. Grosswald, Topics From The Theory of Numbers, 1966, pp. 62-63.

LINKS

Table of n, a(n) for n=1..60.

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

FORMULA

a(n) = -6 + Sum_{k=0..n} ((1/24)*(-5*(k mod 4)+31*((k+1) mod 4)+13*((k+2) mod 4)+13*((k+3) mod 4))), with n>=1. - Paolo P. Lava, Feb 29 2008

G.f.: x*(2 + 4*x + x^2 + 4*x^3 + 2*x^4)/(1 - x - x^4 + x^5). - Philippe Deléham, Dec 01 2016

EXAMPLE

2^11 - 7 = 2041 = 11*157. Thus 2 is in the sequence.

MATHEMATICA

LinearRecurrence[{1, 0, 0, 1, -1}, {2, 6, 7, 11, 15}, 60] (* Ray Chandler, Aug 25 2015 *)

PROG

(PARI) conxkmap(a, p, n) = { for(x=1, n, for(j=1, n, y=x^j-a; if(y%p==0, print1(x", "); break) ) ) }

(MAGMA) I:=[2, 6, 7, 11, 15]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, Dec 02 2016

CROSSREFS

Sequence in context: A032926 A214991 A286995 * A231500 A174000 A241720

Adjacent sequences:  A088224 A088225 A088226 * A088228 A088229 A088230

KEYWORD

nonn,easy

AUTHOR

Cino Hilliard, Nov 03 2003

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)