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a(n) = 3*n^2 + 27*n + 1.
1

%I #21 Jan 31 2023 08:30:34

%S 31,67,109,157,211,271,337,409,487,571,661,757,859,967,1081,1201,1327,

%T 1459,1597,1741,1891,2047,2209,2377,2551,2731,2917,3109,3307,3511,

%U 3721,3937,4159,4387,4621,4861,5107,5359,5617,5881,6151,6427,6709,6997,7291

%N a(n) = 3*n^2 + 27*n + 1.

%C The values of a(n) for 1 <= n <= 14 are primes, a(15) = 1081 = 23*47.

%H G. C. Greubel, <a href="/A110831/b110831.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _G. C. Greubel_, Oct 19 2017: (Start)

%F G.f.: x*(31 - 24*x + x^2)/(1 - x)^3.

%F E.g.f.: (1 + 30*x + 3*x^2)*exp(x) - 1. (End)

%F Sum_{n>=1} 1/a(n) = tan(sqrt(239/3)*Pi/2)*Pi/sqrt(717) - 2643017/2948761. - _Amiram Eldar_, Jan 31 2023

%t Table[3*n^2 + 27*n + 1, {n, 100}]

%o (PARI) a(n)=3*n^2+27*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [3*n^2 + 27*n + 1: n in [1..25]]; // _G. C. Greubel_, Oct 19 2017

%K easy,nonn

%O 1,1

%A Joao da Silva (zxawyh66(AT)yahoo.com), Sep 16 2005

%E Edited by _Arkadiusz Wesolowski_, Oct 11 2011