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%I #24 Sep 08 2022 08:45:01
%S 1,5,11,109,3607,37783
%N Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 61 for n > 0.
%C Numbers n such that (830*10^n + 61)/9 is prime. - _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
%C Numbers n such that digit 9 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.
%C Numbers corresponding to terms <= 3607 are certified primes. For number corresponding to 37783 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#pdp929">PDP Reference Table - 929</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/92229.htm#prime">Prime numbers of the form 922...229</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A082718(n) - 2.
%e 9222229 is prime, hence 5 is a term.
%t Do[If[PrimeQ[(9*10^n + 2*(10^n - 1)/9)*10 + 9], Print[n]], {n, 1, 2500}]
%t Select[Range[2000], PrimeQ[(830 10^# + 61) / 9] &] (* _Vincenzo Librandi_, Nov 02 2014 *)
%o (PARI) a=99;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-61) \\ _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
%o (PARI) for(n=0,1000,if(isprime((830*10^n + 61)/9),print1(n,","))) \\ _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
%o (Magma) [n: n in [0..1000] | IsPrime((830*10^n + 61) div 9)]; // _Vincenzo Librandi_, Nov 02 2014
%Y Cf. A000533, A002275, A068651, A082718.
%K hard,nonn,more
%O 1,2
%A _Robert G. Wilson v_, Aug 18 2000
%E 3607 from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
%E 37783 from _Patrick De Geest_, Jun 26 2005
%E Edited by _N. J. A. Sloane_, Jan 14 2008
%E Edited by _Ray Chandler_, Oct 20 2010
%E Comments section edited by _Patrick De Geest_, Nov 02 2014
%E Editied by _Ray Chandler_, Nov 05 2014
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