OFFSET
1,1
COMMENTS
The first 6 terms are prime, so are the 9th, 10th, 13th, 14th, 15th, 18th, 20th, and 26th.
Any term of the form a(7+n*10) appears to be divisible by 11.
Any term of the form a(11+n*12) appears to be divisible by 13.
Any term of the form a(1+n*22) appears to be divisible by 23.
Any term that is not prime appears to have its factors recurring periodically in the sequence as factors of higher terms.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = 3*2^(n+3)-25 = A007283(n+3)-25.
a(n+1) = a(n)+3*2^(n+3) with a(1) = 23.
a(n) = 3*a(n-1)-2*a(n-2). - Colin Barker, Mar 05 2015
G.f.: x*(2*x+23) / ((x-1)*(2*x-1)). - Colin Barker, Mar 05 2015
MATHEMATICA
Table[3*2^(n + 3) - 25, {n, 1, k}]
LinearRecurrence[{3, -2}, {23, 71}, 30] (* Harvey P. Dale, Apr 10 2021 *)
PROG
(PARI) Vec(x*(2*x+23)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 05 2015
(Magma) [3*2^(n + 3) - 25: n in [1..30]]; // Vincenzo Librandi, Mar 08 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zeid Ghalyoun, Mar 05 2015
STATUS
approved