A060566 a(n) = n^2 - 79*n + 1601.

1601, 1523, 1447, 1373, 1301, 1231, 1163, 1097, 1033, 971, 911, 853, 797, 743, 691, 641, 593, 547, 503, 461, 421, 383, 347, 313, 281, 251, 223, 197, 173, 151, 131, 113, 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

Offset: 0

Author

Jason Earls, Apr 11 2001

Keywords

• easy
• nonn

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.
• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 115.

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).

Crossrefs

Cf. A002837, A005846, A202018.

Programs

Magma

[n^2-79*n+1601: n in [0..80]]; // Vincenzo Librandi, Feb 27 2017

Maple

A060566:=n->n^2-79*n+1601: seq(A060566(n), n=0..150); # Wesley Ivan Hurt, Jul 10 2017

Mathematica

Table[n^2-79*n+1601,{n,100}] (* or *) LinearRecurrence[{3,-3,1},{1523,1447,1373},100] (* Harvey P. Dale, Jan 14 2017 *)

PARI

a(n) = { n^2 - 79*n + 1601 } \\ Harry J. Smith, Jul 07 2009

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

E.g.f.: exp(x)*(1601 - 78*x + x^2). - Elmo R. Oliveira, Feb 09 2025

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 16 2007

a(125) in b-file corrected by Andrew Howroyd, Feb 21 2018