A088225 Solutions to x^n == 7 (mod 11).

2, 6, 7, 8, 13, 17, 18, 19, 24, 28, 29, 30, 35, 39, 40, 41, 46, 50, 51, 52, 57, 61, 62, 63, 68, 72, 73, 74, 79, 83, 84, 85, 90, 94, 95, 96, 101, 105, 106, 107, 112, 116, 117, 118, 123, 127, 128, 129, 134, 138, 139, 140, 145, 149, 150, 151, 156, 160, 161, 162, 167, 171

Offset

1,1

Comments

Also, numbers congruent to {2, 6, 7, 8} mod 11. - Bruno Berselli, Jan 20 2016

References

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5. - Harvey P. Dale, Jan 30 2015

From Colin Barker, Oct 16 2015: (Start)

a(n) = (-9 - (-1)^n - (7-i)*(-i)^n - (7+i)*i^n + 22*n)/8, where i=sqrt(-1).

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

Example

2^7 - 7 = 121 = 11*11. Thus 2 is in the sequence.
13^7 - 7 = 11*5704410. Thus 13 is in the sequence.

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {2, 6, 7, 8, 13}, 70] (* Harvey P. Dale, Jan 30 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) ) ) }
(PARI) a(n) = (-9 - (-1)^n - (7-I)*(-I)^n - (7+I)*I^n + 22*n)/8 \\ Colin Barker, Oct 16 2015
(PARI) Vec(x*(3*x^4+x^3+x^2+4*x+2)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Oct 16 2015

Crossrefs

Sequence in context: A048859 A026311 A063291 * A165775 A258826 A157671

Adjacent sequences: A088222 A088223 A088224 * A088226 A088227 A088228

Keyword

nonn,easy

Author

Cino Hilliard, Nov 03 2003

Status

approved