A096209 -id:A096209 - cp's OEIS frontend

A111391 Numbers k such that 11*10^k - 1 is prime.

1, 9, 11, 17, 22, 29, 36, 37, 52, 166, 448, 2011, 3489, 4871, 6982, 10024, 16974, 33287, 47364, 58873, 126160, 234424, 382881, 524706

Offset: 1

Robert G. Wilson v, Nov 15 2005

Numbers k such that 10^(k+1) + (10^k-1) is a prime.

Gary Barnes, Primes of the form k*10^n-1
Makoto Kamada, Search for 109w.

Cf. A096209.

Do[ If[ PrimeQ[10^(n + 1) + (10^n - 1)], Print[n]], {n, 9500}]

is(n)=ispseudoprime(11*10^n-1) \\ Charles R Greathouse IV, Jun 12 2017

a(16)-a(19) from Ray Chandler, Sep 16 2013
a(20)-a(21) from P. Kurtovic submitted by Ray Chandler, Sep 17 2013
a(22)-a(24) from Kamada data by Tyler Busby, Apr 14 2024

A198700 a(n) = 11*10^n - 1.

Original entry on oeis.org

10, 109, 1099, 10999, 109999, 1099999, 10999999, 109999999, 1099999999, 10999999999, 109999999999, 1099999999999, 10999999999999, 109999999999999, 1099999999999999, 10999999999999999, 109999999999999999, 1099999999999999999, 10999999999999999999, 109999999999999999999

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002283, A066007, A109002.

Cf. A096209 (primes).

Magma
```
[11*10^n-1: n in [0..30]];
```

(11 10^Range[0,20])-1 (* or  *) LinearRecurrence[{11,-10},{10,109},20] (* Harvey P. Dale, Nov 29 2020 *)

a(n) = 10*a(n-1) + 9.
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: (10-x)/((10*x-1)*(x-1)). - R. J. Mathar, Oct 29 2011
E.g.f.: exp(x)*(11*exp(9*x) - 1). - Elmo R. Oliveira, Aug 23 2024

A113629 Primes of the form 10 followed by a string of 3's.

Original entry on oeis.org

103, 1033, 10333, 103333, 10333333, 103333333, 1033333333, 10333333333333, 10333333333333333333, 10333333333333333333333333333333, 10333333333333333333333333333333333333333333333333333333333333333333333333333

Offset: 1

Amarnath Murthy, Nov 10 2005

Cf. A113628, A113630, A096209.

More terms from Jim Nastos, Nov 15 2005

cp's OEIS Frontend

A111391 Numbers k such that 11*10^k - 1 is prime.

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A198700 a(n) = 11*10^n - 1.

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A113629 Primes of the form 10 followed by a string of 3's.

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