A186950 a(n) = n^2 - 47*n + 479.

479, 433, 389, 347, 307, 269, 233, 199, 167, 137, 109, 83, 59, 37, 17, -1, -17, -31, -43, -53, -61, -67, -71, -73, -73, -71, -67, -61, -53, -43, -31, -17, -1, 17, 37, 59, 83, 109, 137, 167, 199, 233, 269, 307, 347, 389, 433, 479, 527, 577, 629, 683, 739, 797, 857

Offset: 0

Author

Arkadiusz Wesolowski, Mar 01 2011

Keywords

• easy
• sign

Comments

a(n) are distinct primes for 0 <= n <= 14. There are 22 distinct (positive and negative) values of primes between a(0) = 479 and a(48) = 527.

For n < 15 and n > 32, the prime numbers of this sequence are in A059425. - Bruno Berselli, Mar 04 2011

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..1000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 479.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A059425, A126665.

Programs

Magma

[n^2-47*n+479 : n in [0..53]]; // Arkadiusz Wesolowski, Mar 05 2011

Maple

seq(n^2-47*n+479, n=0..53); # Arkadiusz Wesolowski, Mar 08 2011

Mathematica

Table[n^2 - 47*n + 479, {n, 0, 53}] (* Arkadiusz Wesolowski, Mar 05 2011 *)
LinearRecurrence[{3,-3,1},{479,433,389},60] (* Harvey P. Dale, Nov 28 2018 *)

PARI

for(n=0, 53, print1(n^2-47*n+479, ", ")); \\ Arkadiusz Wesolowski, Mar 02 2011

Formula

G.f.: (479 - 1004*x + 527*x^2)/(1-x)^3. - Bruno Berselli, Mar 05 2011

a(n+19) = -A126665(n). - Arkadiusz Wesolowski, Oct 24 2013

From Elmo R. Oliveira, Nov 02 2024: (Start)

E.g.f.: (479 - 46*x + x^2)*exp(x).

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