A100776 a(n) = 997*n + 1009.

1009, 2006, 3003, 4000, 4997, 5994, 6991, 7988, 8985, 9982, 10979, 11976, 12973, 13970, 14967, 15964, 16961, 17958, 18955, 19952, 20949, 21946, 22943, 23940, 24937, 25934, 26931, 27928, 28925, 29922, 30919, 31916, 32913, 33910, 34907, 35904, 36901, 37898, 38895

Offset

0,1

Comments

Note that 997 is the largest three-digit prime and 1009 is the smallest four-digit prime.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Tanya Khovanova, Recursive Sequences.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

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

G.f.: (1009 - 12*x)/(1 - x)^2.

E.g.f.: (1009 + 997*x)*exp(x).

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

Example

If n=1, 997*1 + 1009 = 2006.
If n=2, 997*2 + 1009 = 3003.

Maple

A100776:=n->997 * n + 1009; seq(A100776(n), n=0..50); # Wesley Ivan Hurt, Jan 22 2014

Mathematica

Table[997 n + 1009, {n, 0, 50}] (* Wesley Ivan Hurt, Jan 22 2014 *)

Prog

(Magma) [997 * n + 1009: n in [0..50]]; // Vincenzo Librandi, Jul 14 2011
(PARI) a(n)=997*n+1009 \\ Charles R Greathouse IV, Jul 10 2016

Crossrefs

Cf. A017029, A100775, A101086, A101442.

Sequence in context: A024974 A025400 A182695 * A126238 A176930 A308793

Adjacent sequences: A100773 A100774 A100775 * A100777 A100778 A100779

Keyword

nonn,easy

Author

Parthasarathy Nambi, Jan 03 2005

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005

Edited by Ray Chandler, Jan 25 2005

Status

approved