OFFSET
0,1
COMMENTS
See A270971 for the motivation.
These are all Sierpiński numbers.
Since 9454129 is a term of A244561, for every integer k > 0, 9454129*2^k + 1 has a divisor in the set {3, 5, 7, 13, 17, 241}. And because 11184810 = 2*3*5*7*13*17*241, a(n)*2^k + 1 = 9454129*2^k + 1 + 11184810*n*2^k + 1 always has a divisor in the set {3, 5, 7, 13, 17, 241}. Since a(n) is always odd because of its definition, a(n) is a Sierpiński number.
Also 9454129 + 28 = 9454157 is a term of A244561. So, with the same proof, a(n) + 28 is a Sierpiński number too.
Are a(n) and a(n) + 28 always consecutive Sierpiński numbers?
LINKS
FORMULA
G.f.: (9454129 + 1730681*x)/(1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n > 1.
EXAMPLE
a(1) = 9454129 + 11184810*1 = 20638939.
MAPLE
MATHEMATICA
Table[9454129 + 11184810*n, {n, 0, 100}] (* G. C. Greubel, Mar 28 2016 *)
PROG
(PARI) a(n) = 9454129 + 11184810*n;
(PARI) x='x+O('x^99); Vec((9454129+1730681*x)/(1-x)^2)
(Magma) [9454129 + 11184810*n: n in [0..30]]; // Vincenzo Librandi, Mar 29 2016
(Python) for n in range(0, 100):print(9454129+11184810*n) # Soumil Mandal, Apr 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Mar 28 2016
STATUS
approved