|
%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
| 