OFFSET
0,1
COMMENTS
a(n) is prime for 0 <= n <= 79. a(80) = 1681 = 41^2.
More than the usual number of terms are shown in order to display the initial 80 primes.
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
REFERENCES
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Dover Publications, NY, 1966, p. 37, 147.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000 (terms 0..500 from Harry J. Smith and Miquel Cerda)
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
From Vincenzo Librandi, Feb 27 2017: (Start)
G.f.: (1601 - 3280*x + 1681*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
(End)
a(n) = (n-40)^2 + (n-40) + 41. - Miquel Cerda, Jul 10 2017
MAPLE
MATHEMATICA
Table[n^2-79*n+1601, {n, 100}] (* or *) LinearRecurrence[{3, -3, 1}, {1523, 1447, 1373}, 100] (* Harvey P. Dale, Jan 14 2017 *)
PROG
(PARI) a(n) = { n^2 - 79*n + 1601 } \\ Harry J. Smith, Jul 07 2009
(MAGMA) [n^2-79*n+1601: n in [0..80]]; // Vincenzo Librandi, Feb 27 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Apr 11 2001
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew Plewe, May 16 2007
a(125) in b-file corrected by Andrew Howroyd, Feb 21 2018
STATUS
editing