A127316 a(n) = 2*n^2 - 4*n + 73.
71, 73, 79, 89, 103, 121, 143, 169, 199, 233, 271, 313, 359, 409, 463, 521, 583, 649, 719, 793, 871, 953, 1039, 1129, 1223, 1321, 1423, 1529, 1639, 1753, 1871, 1993, 2119, 2249, 2383, 2521, 2663, 2809, 2959, 3113, 3271, 3433, 3599, 3769, 3943, 4121, 4303, 4489
Offset: 1
Examples
If n=10 then 2*n^2 - 4*n + 73 = 233.
Links
- Michael M. Ross, Poly Primes: The Polynomiality of Proximate Primes.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
Magma
[2*n^2-4*n+73 : n in [1..48]]; // Arkadiusz Wesolowski, Oct 24 2013
-
Mathematica
Table[2*n^2 - 4*n + 73, {n, 48}] (* Arkadiusz Wesolowski, Oct 24 2013 *) -
PARI
vector(48, n, 2*n^2-4*n+73) \\ Arkadiusz Wesolowski, Oct 24 2013
Formula
G.f.: x*(71 - 140*x + 73*x^2)/(1 - x)^3. - Arkadiusz Wesolowski, Oct 24 2013
Sum_{n>=1} 1/a(n) = 1/142 + coth(sqrt(71/2)*Pi)/(2*sqrt(142)). - Amiram Eldar, Jul 30 2024
From Elmo R. Oliveira, Nov 03 2024: (Start)
E.g.f.: exp(x)*(2*x^2 - 2*x + 73) - 73.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
Extensions
Extended by Charles R Greathouse IV, Jul 25 2010
Comments