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
References
- A prime-generating quadratic: the absolute values are primes for 0 <= n <= 39.
Links
- Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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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:
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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 *) -
PARI
a(n)=111*n^2-3123*n+10753 \\ Charles R Greathouse IV, Feb 12 2013
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)