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%I #15 Jan 17 2019 13:44:06
%S 0,1,2,5,11,19,20,36,41,54,59,97,99,103,222,236,259,500,569,599,697,
%T 8856,20910,24344,31963,67741,162923
%N Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 81 for n > 0.
%C Numbers n such that 80*10^n + 9 is prime.
%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 0 followed by digit 9 is prime.
%C Numbers corresponding to terms <= 697 are certified primes.
%C a(28) > 2*10^5. - _Robert Price_, Dec 18 2015
%D Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/8/80009.htm#prime">Prime numbers of the form 800...009</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A103070(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%e 8000009 is prime, hence 5 is a term.
%t Do[If[PrimeQ[80*10^n + 9], Print[n]], {n, 0, 20000}] (* _Robert Price_, Dec 18 2015 *)
%o (PARI) a=89;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-81)
%o (PARI) for(n=0,1000,if(isprime(80*10^n + 9),print1(n,",")))
%Y Cf. A000533, A002275, A103070.
%K nonn,hard,more
%O 1,3
%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004
%E 8856 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E a(23)-a(26) from Kamada data by _Ray Chandler_, Apr 29 2015
%E a(27) from _Robert Price_, Dec 18 2015
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