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URL: https://oeis.org/A101442

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A101442

a(n) = 9973*n + 10007.

4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

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)

EXAMPLE

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A017029, A100775, A100776, A101444.

Sequence in context: A164968 A165296 A182697 * A173029 A256838 A176931

Adjacent sequences: A101439 A101440 A101441 * A101443 A101444 A101445

KEYWORD

nonn,easy,less

AUTHOR

Parthasarathy Nambi, Jan 18 2005

EXTENSIONS

Extended by Ray Chandler, Jan 25 2005

STATUS

approved