A056266 - OEIS

%I #22 Sep 08 2022 08:45:01

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

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

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

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

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

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

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp989">PDP Reference Table - 989</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/98889.htm#prime">Prime numbers of the form 988...889</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

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

%e 9888889 is prime, hence 5 is a term.

%t Select[Range[2000], PrimeQ[(890 10^# + 1) / 9] &] (* _Vincenzo Librandi_, Nov 02 2014 *)

%o (PARI) a=99;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-1)

%o (PARI) for(n=0,1500,if(isprime((890*10^n+1)/9),print1(n,",")))

%o (Magma) [n: n in [0..1000] | IsPrime((890*10^n+1) div 9)]; // _Vincenzo Librandi_, Nov 02 2014

%Y Cf. A000533, A002275, A056728, A082719.

%K nonn,hard,more

%O 1,1

%A _Robert G. Wilson v_, Aug 18 2000

%E Additional comments from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

%E Edited by _N. J. A. Sloane_, Apr 17 2007

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

%E Two more terms from PDP table added and comments section edited by _Patrick De Geest_, Nov 02 2014

%E Edited by _Ray Chandler_, Nov 05 2014