A056266 Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 1 for n > 0.

5, 71, 95, 113, 203, 983, 1225, 4793, 20719, 133579, 411589

Offset

1,1

Comments

Numbers n such that (890*10^n + 1)/9 is prime.

Numbers n such that the number 9 8(n times) 9 is prime.

Numbers corresponding to terms <= 983 are certified primes. For numbers greater than 4793, see P. De Geest, PDP Reference Table.

References

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

Table of n, a(n) for n=1..11.

Patrick De Geest, PDP Reference Table - 989.

Makoto Kamada, Prime numbers of the form 988...889.

Index entries for primes involving repunits.

Formula

a(n) = A082719(n) - 2.

Example

9888889 is prime, hence 5 is a term.

Mathematica

Select[Range[2000], PrimeQ[(890 10^# + 1) / 9] &] (* Vincenzo Librandi, Nov 02 2014 *)

Prog

(PARI) a=99; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-1)
(PARI) for(n=0, 1500, if(isprime((890*10^n+1)/9), print1(n, ", ")))
(Magma) [n: n in [0..1000] | IsPrime((890*10^n+1) div 9)]; // Vincenzo Librandi, Nov 02 2014

Crossrefs

Cf. A000533, A002275, A056728, A082719.

Sequence in context: A324229 A338989 A101019 * A248367 A157860 A125242

Adjacent sequences: A056263 A056264 A056265 * A056267 A056268 A056269

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Aug 18 2000

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Edited by N. J. A. Sloane, Apr 17 2007

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Two more terms from PDP table added and comments section edited by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 05 2014

Status

approved