OFFSET
1,2
COMMENTS
Numbers of the form d*13^j for d a divisor of 12.
REFERENCES
Trygve Nagell, Introduction to Number Theory. New York: Wiley, 1951, pp. 164-168.
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..500
Eric Weisstein, Cyclotomic Polynomial.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,13).
FORMULA
a(n) = 13*a(n-6). G.f.: -x*(12*x^5+6*x^4+4*x^3+3*x^2+2*x+1) / (13*x^6-1). - Colin Barker, Jul 30 2014
EXAMPLE
The 4th cyclotomic polynomial x^2 + 1 considered modulo 13 has a root x = 5, so 4 is in the sequence.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 13}, {1, 2, 3, 4, 6, 12}, 50] (* Harvey P. Dale, Aug 19 2021 *)
PROG
(Sage) def A245481(n) : return [12, 1, 2, 3, 4, 6][n%6]*13^((n-1)//6)
(PARI) for(n=1, 10^6, if(#polrootsmod(polcyclo(n), 13), print1(n, ", "))) /* by definition; rather inefficient. - Joerg Arndt, Jul 28 2014 */
(PARI) Vec(-x*(12*x^5+6*x^4+4*x^3+3*x^2+2*x+1)/(13*x^6-1) + O(x^100)) \\ Colin Barker, Jul 30 2014
(PARI) a(n)=[12, 1, 2, 3, 4, 6][n%6+1]*13^((n-1)\6) \\ Charles R Greathouse IV, Jan 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric M. Schmidt, Jul 23 2014
STATUS
approved