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

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

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.

Examples

			9888889 is prime, hence 5 is a term.
		

References

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

Links

• Patrick De Geest, PDP Reference Table - 989.
• Makoto Kamada, Prime numbers of the form 988...889.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A056728, A082719.

Programs

Magma

[n: n in [0..1000] | IsPrime((890*10^n+1) div 9)]; // Vincenzo Librandi, Nov 02 2014

Mathematica

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

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,",")))

Formula

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

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