This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060566 #52 Jul 16 2025 10:05:10
%S A060566 1601,1523,1447,1373,1301,1231,1163,1097,1033,971,911,853,797,743,691,
%T A060566 641,593,547,503,461,421,383,347,313,281,251,223,197,173,151,131,113,
%U A060566 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 A060566 a(n) = n^2 - 79*n + 1601.
%C A060566 a(n) is prime for 0 <= n <= 79. a(80) = 1681 = 41^2.
%C A060566 More than the usual number of terms are shown in order to display the initial 80 primes.
%C A060566 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 A060566 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.
%D A060566 C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Dover Publications, NY, 1966, p. 37, 147.
%D A060566 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 115.
%H A060566 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 A060566 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A060566 From _Vincenzo Librandi_, Feb 27 2017: (Start)
%F A060566 G.f.: (1601 - 3280*x + 1681*x^2)/(1 - x)^3.
%F A060566 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A060566 a(n) = (n-40)^2 + (n-40) + 41. - _Miquel Cerda_, Jul 10 2017
%F A060566 E.g.f.: exp(x)*(1601 - 78*x + x^2). - _Elmo R. Oliveira_, Feb 09 2025
%p A060566 A060566:=n->n^2-79*n+1601: seq(A060566(n), n=0..150); # _Wesley Ivan Hurt_, Jul 10 2017
%t A060566 Table[n^2-79*n+1601,{n,100}] (* or *) LinearRecurrence[{3,-3,1},{1523,1447,1373},100] (* _Harvey P. Dale_, Jan 14 2017 *)
%o A060566 (PARI) a(n) = { n^2 - 79*n + 1601 } \\ _Harry J. Smith_, Jul 07 2009
%o A060566 (Magma) [n^2-79*n+1601: n in [0..80]]; // _Vincenzo Librandi_, Feb 27 2017
%Y A060566 Cf. A002837, A005846, A202018.
%K A060566 easy,nonn
%O A060566 0,1
%A A060566 _Jason Earls_, Apr 11 2001
%E A060566 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 16 2007
%E A060566 a(125) in b-file corrected by _Andrew Howroyd_, Feb 21 2018