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
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Nov 03 2003
STATUS
approved