A216257 a(n) = 840*n^2 - 23100*n + 86861.

86861, 64601, 44021, 25121, 7901, -7639, -21499, -33679, -44179, -52999, -60139, -65599, -69379, -71479, -71899, -70639, -67699, -63079, -56779, -48799, -39139, -27799, -14779, -79, 16301, 34361, 54101, 75521, 98621, 123401, 149861, 178001, 207821, 239321, 272501

Offset: 0

Author

Arkadiusz Wesolowski, Mar 15 2013

Keywords

• easy
• sign

Comments

|a(n)| are distinct primes for 0 <= n <= 32.

The values of this polynomial are never divisible by a prime less than 79.

All terms are congruent to 1 (mod 20).

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A141881, A141887, A215145.

Programs

Magma

[ 840*n^2-23100*n+86861 : n in [0..34]];

Maple

seq(840*n^2-23100*n+86861, n=0..34);

Mathematica

Table[840*n^2 - 23100*n + 86861, {n, 0, 34}]

PARI

for(n=0, 34, print1(840*n^2-23100*n+86861, ", "))

Formula

G.f.: (86861 - 195982*x + 110801*x^2)/(1-x)^3.

From Elmo R. Oliveira, Feb 10 2025: (Start)

E.g.f.: exp(x)*(86861 - 22260*x + 840*x^2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)