A270994 a(n) = 9454129 + 11184810*n.

9454129, 20638939, 31823749, 43008559, 54193369, 65378179, 76562989, 87747799, 98932609, 110117419, 121302229, 132487039, 143671849, 154856659, 166041469, 177226279, 188411089, 199595899, 210780709, 221965519, 233150329, 244335139, 255519949, 266704759, 277889569, 289074379, 300259189

Offset: 0

Author

Altug Alkan, Mar 28 2016

Keywords

• nonn
• easy

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?

Examples

			a(1) = 9454129 + 11184810*1 = 20638939.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A076336, A244561, A270971, A270993.

Programs

Magma

[9454129 + 11184810*n: n in [0..30]]; // Vincenzo Librandi, Mar 29 2016

Maple

A270994:=n->9454129 + 11184810*n: seq(A270994(n), n=0..40); # Wesley Ivan Hurt, Apr 02 2016

Mathematica

Table[9454129 + 11184810*n, {n, 0, 100}] (* G. C. Greubel, Mar 28 2016 *)

PARI

a(n) = 9454129 + 11184810*n;

PARI

x='x+O('x^99); Vec((9454129+1730681*x)/(1-x)^2)

Python

for n in range(0,100):print(9454129+11184810*n) # Soumil Mandal, Apr 03 2016

Formula

G.f.: (9454129 + 1730681*x)/(1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n > 1.