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

1,1

Comments

Extrapolates a quadratic passing through 71, 73, and 79.

Links

Table of n, a(n) for n=1..48.

Michael M. Ross, Poly Primes: The Polynomiality of Proximate Primes.

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

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)

Example

If n=10 then 2*n^2 - 4*n + 73 = 233.

Mathematica

Table[2*n^2 - 4*n + 73, {n, 48}] (* Arkadiusz Wesolowski, Oct 24 2013 *)

Prog

(Magma) [2*n^2-4*n+73 : n in [1..48]]; // Arkadiusz Wesolowski, Oct 24 2013
(PARI) vector(48, n, 2*n^2-4*n+73) \\ Arkadiusz Wesolowski, Oct 24 2013

Crossrefs

Cf. A126665, A126719.

Sequence in context: A095936 A104843 A322831 * A322444 A339700 A217414

Adjacent sequences: A127313 A127314 A127315 * A127317 A127318 A127319

Keyword

easy,nonn

Author

Michael M. Ross, Mar 28 2007

Extensions

Extended by Charles R Greathouse IV, Jul 25 2010

Status

approved