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
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).
Programs
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Magma
[3*10^n+1: n in [0..30]];
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Mathematica
3*10^Range[0,20]+1 (* or *) LinearRecurrence[{11,-10},{4,31},20] (* Harvey P. Dale, Dec 12 2016 *)
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