A226097 a(n) = ((-1)^n + 2*n - 38)*(2*n - 38) + 41.

1447, 1373, 1163, 1097, 911, 853, 691, 641, 503, 461, 347, 313, 223, 197, 131, 113, 71, 61, 43, 41, 47, 53, 83, 97, 151, 173, 251, 281, 383, 421, 547, 593, 743, 797, 971, 1033, 1231, 1301, 1523, 1601, 1847, 1933, 2203, 2297, 2591, 2693, 3011, 3121, 3463, 3581, 3947

Offset: 0

Author

Arkadiusz Wesolowski, May 26 2013

Keywords

• nonn
• easy

Comments

a(n) are distinct primes for n = 0 to 59.

All terms are in A202018.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..1000
• Carlos Rivera, Puzzle 782
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A000040, A005846, A060566, A202018.

Programs

Magma

[((-1)^n+a)*a+41 where a is 2*n-38 : n in [0..50]];

Mathematica

g[n_] := 2*n - 38; f[n_] := ((-1)^n + g[n])*g[n] + 41; Table[f[n], {n, 0, 50}]
EulerP[n_] := n^2 - n + 41; f[n_] := 2*n - (3 + (-1)^n)/2; LinearRecurrence[{1, 2, -2, -1, 1}, Table[EulerP@f[n], {n, 19, 15, -1}], {0, 50}]

PARI

Vec((1447 - 74*x - 3104*x^2 + 82*x^3 + 1681*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^100)) \\ Colin Barker, Aug 14 2017

Formula

G.f.: (1447-2*x*(37+1552*x-41*x^2)+(41*x^2)^2)/((1+x)^2*(1-x)^3).

From Colin Barker, Aug 14 2017: (Start)

G.f.: (1447 - 74*x - 3104*x^2 + 82*x^3 + 1681*x^4) / ((1 - x)^3*(1 + x)^2).

a(n) = 4*n^2 - 150*n + 1447 for n even.

a(n) = 4*n^2 - 154*n + 1523 for n odd.

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.

(End)