Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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