A267706 a(n) = 137*n^2 - 4043*n + 27277.

27277, 23371, 19739, 16381, 13297, 10487, 7951, 5689, 3701, 1987, 547, -619, -1511, -2129, -2473, -2543, -2339, -1861, -1109, -83, 1217, 2791, 4639, 6761, 9157, 11827, 14771, 17989, 21481, 25247, 29287, 33601, 38189, 43051, 48187, 53597, 59281, 65239, 71471, 77977

Offset

0,1

Comments

|a(n)| are distinct primes for 0 <= n <= 39.

The values of this polynomial are never divisible by a prime less than 59.

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).

Formula

G.f.: (27277 - 58460*x + 31457*x^2)/(1-x)^3.

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

E.g.f.: exp(x)*(27277 - 3906*x + 137*x^2).

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

Maple

seq(137*n^2-4043*n+27277, n=0..39);

Mathematica

Table[137*n^2 - 4043*n + 27277, {n, 0, 39}]

Prog

(Magma) [137*n^2-4043*n+27277: n in [0..39]];
(PARI) for(n=0, 39, print1(137*n^2-4043*n+27277, ", "));

Crossrefs

Sequence in context: A251777 A032746 A099230 * A237381 A109481 A328214

Adjacent sequences: A267703 A267704 A267705 * A267707 A267708 A267709

Keyword

sign,easy

Author

Arkadiusz Wesolowski, Jan 30 2016

Status

approved