A199683 a(n) = 3*10^n + 1.

4, 31, 301, 3001, 30001, 300001, 3000001, 30000001, 300000001, 3000000001, 30000000001, 300000000001, 3000000000001, 30000000000001, 300000000000001, 3000000000000001, 30000000000000001, 300000000000000001, 3000000000000000001, 30000000000000000001, 300000000000000000001

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.

S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Formula

a(n) = 10*a(n-1) - 9.

a(n) = 11*a(n-1) - 10*a(n-2).

G.f.: (4-13*x)/((1-x)*(1-10*x)).

E.g.f.: exp(x)*(1 + 3*exp(9*x)). - Elmo R. Oliveira, Jun 10 2025

Mathematica

3*10^Range[0, 20]+1 (* Harvey P. Dale, Dec 12 2016 *)
(* Alternative: *)
LinearRecurrence[{11, -10}, {4, 31}, 20] (* Harvey P. Dale, Dec 12 2016 *)

Prog

(Magma) [3*10^n+1: n in [0..30]];

Crossrefs

Primes: A056807, A259866.

Sequence in context: A307504 A371362 A276316 * A375434 A114475 A243312

Adjacent sequences: A199680 A199681 A199682 * A199684 A199685 A199686

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Nov 09 2011

Status

approved