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%I #19 Jan 17 2019 13:44:06
%S 0,1,7,16,18,24,39,48,57,58,91,112,295,636,1855,2514,3592,6990,11839,
%T 86071,93507
%N Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 31 for n > 0.
%C Numbers n such that (770*10^n + 31)/9 is prime.
%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.
%C Numbers corresponding to terms <= 636 are certified primes.
%C a(22) > 10^5. - _Robert Price_, Oct 26 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/8/85559.htm#prime">Prime numbers of the form 855...559</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A103086(n) - 1.
%e 855555559 is prime, hence 7 is a term.
%t Flatten[Position[NestList[10#-31&,89,1000],_?PrimeQ]-1] (* As written, the program will generate the first 14 terms of the sequence; changing the constant from 1000 to 7000 will generate 18 terms of the sequence but it will take a long time to do so *) (* _Harvey P. Dale_, Jul 16 2012 *)
%t Select[Range[0, 100000], PrimeQ[(770*10^# + 31)/9] &] (* _Robert Price_, Oct 26 2015 *)
%o (PARI) a=89;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-31)
%o (PARI) for(n=0,1000,if(isprime((770*10^n+31)/9),print1(n,",")))
%Y Cf. A000533, A002275, A103086.
%K nonn,hard,more
%O 1,3
%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E a(19) from Kamada data by _Ray Chandler_, Apr 29 2015
%E a(20)-a(21) from _Robert Price_, Oct 26 2015
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