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%I #45 Sep 08 2022 08:45:03
%S 1601,1523,1447,1373,1301,1231,1163,1097,1033,971,911,853,797,743,691,
%T 641,593,547,503,461,421,383,347,313,281,251,223,197,173,151,131,113,
%U 97,83,71,61,53,47,43,41,41,43,47,53,61,71,83,97,113,131,151,173,197,223,251,281,313,347,383,421,461,503,547,593,641,691,743,797,853,911,971,1033,1097,1163,1231,1301,1373,1447,1523,1601,1681
%N a(n) = n^2 - 79*n + 1601.
%C a(n) is prime for 0 <= n <= 79. a(80) = 1681 = 41^2.
%C More than the usual number of terms are shown in order to display the initial 80 primes.
%C First 80 prime entries are palindromically distributed because a(n) = P(x) = x^2 + x + 41, with x=n-40 and we observe that P(x) generates primes (A005846) for x = 0 through 39, along with the fact that P(-x) = P(x-1). - _Lekraj Beedassy_, Apr 24 2006
%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.
%D C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Dover Publications, NY, 1966, p. 37, 147.
%H Andrew Howroyd, <a href="/A060566/b060566.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..500 from Harry J. Smith and Miquel Cerda)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F From _Vincenzo Librandi_, Feb 27 2017: (Start)
%F G.f.: (1601 - 3280*x + 1681*x^2)/(1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F (End)
%F a(n) = (n-40)^2 + (n-40) + 41. - _Miquel Cerda_, Jul 10 2017
%p A060566:=n->n^2-79*n+1601: seq(A060566(n), n=0..150); # _Wesley Ivan Hurt_, Jul 10 2017
%t Table[n^2-79*n+1601,{n,100}] (* or *) LinearRecurrence[{3,-3,1},{1523,1447,1373},100] (* _Harvey P. Dale_, Jan 14 2017 *)
%o (PARI) a(n) = { n^2 - 79*n + 1601 } \\ _Harry J. Smith_, Jul 07 2009
%o (Magma) [n^2-79*n+1601: n in [0..80]]; // _Vincenzo Librandi_, Feb 27 2017
%Y Cf. A002837, A202018.
%K easy,nonn
%O 0,1
%A _Jason Earls_, Apr 11 2001
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 16 2007
%E a(125) in b-file corrected by _Andrew Howroyd_, Feb 21 2018
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