A211607 a(n) = 111*n^2 - 3123*n + 10753.

10753, 7741, 4951, 2383, 37, -2087, -3989, -5669, -7127, -8363, -9377, -10169, -10739, -11087, -11213, -11117, -10799, -10259, -9497, -8513, -7307, -5879, -4229, -2357, -263, 2053, 4591, 7351, 10333, 13537, 16963, 20611, 24481, 28573, 32887, 37423, 42181, 47161, 52363, 57787

Offset

0,1

References

A prime-generating quadratic: the absolute values are primes for 0 <= n <= 39.

Links

Table of n, a(n) for n=0..39.

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 111*n^2 - 3123*n + 10753.

G.f.: -(13987*x^2-24518*x+10753)/(x-1)^3. - Colin Barker, Feb 16 2013

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(10753 - 3012*x + 111*x^2).

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

Maple

proc(i)
local a, n;
for n from 0 to i do a:=111*n^2-3123*n+10753; if isprime(abs(a)) then
print(a); fi; od; end:

Mathematica

Table[111n^2 - 3123n + 10753, {n, 0, 39}] (* Alonso del Arte, Feb 13 2013 *)
LinearRecurrence[{3, -3, 1}, {10753, 7741, 4951}, 40] (* Harvey P. Dale, Dec 04 2015 *)

Prog

(PARI) a(n)=111*n^2-3123*n+10753 \\ Charles R Greathouse IV, Feb 12 2013

Crossrefs

Cf. A005846, A050268, A128878, A217439, A217440.

Sequence in context: A255031 A256949 A146320 * A258513 A258506 A254993

Adjacent sequences: A211604 A211605 A211606 * A211608 A211609 A211610

Keyword

sign,easy

Author

Yusuf Z Gurtas, Feb 10 2013

Status

approved