A101442 a(n) = 9973*n + 10007.

10007, 19980, 29953, 39926, 49899, 59872, 69845, 79818, 89791, 99764, 109737, 119710, 129683, 139656, 149629, 159602, 169575, 179548, 189521, 199494, 209467, 219440, 229413, 239386, 249359, 259332, 269305, 279278, 289251, 299224, 309197, 319170, 329143, 339116

Offset: 0

Author

Parthasarathy Nambi, Jan 18 2005

Keywords

• nonn
• easy
• less

Comments

9973 is the largest four-digit prime and 10007 is the smallest five-digit prime.

Examples

			If n=14, then 9973*14 + 10007 = 149629 (a prime).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Chris Caldwell, The first 100,008 primes.
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A017029, A100775, A100776, A101444.

Programs

Magma

[9973*n + 10007: n in [0..50]]; // Vincenzo Librandi, Jul 14 2011

Mathematica

9973*Range[0,30]+10007 (* or *) LinearRecurrence[{2,-1},{10007,19980},40] (* Harvey P. Dale, Sep 02 2015 *)

PARI

a(n)=9973*n+10007 \\ Charles R Greathouse IV, Oct 16 2015

Formula

From Elmo R. Oliveira, Dec 07 2024: (Start)

G.f.: (10007 - 34*x)/(1 - x)^2.

E.g.f.: (10007 + 9973*x)*exp(x).

a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)

Extensions

Extended by Ray Chandler, Jan 25 2005