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%I #17 Jan 17 2019 13:44:06
%S 0,1,3,8,9,14,43,54,55,123,139,278,673,847,1419,1461,3313,3441,4140,
%T 35624
%N Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 51 for n > 0.
%C Numbers n such that (750*10^n + 51)/9 is prime.
%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 3 followed by digit 9 is prime.
%C Numbers corresponding to terms <= 847 are certified primes.
%C a(21) > 10^5. - Robert Price, Oct 20 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/8/83339.htm#prime">Prime numbers of the form 833...339</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A103078(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%e 83339 is prime, hence 3 is a term.
%t Flatten[Position[NestList[10#-51&,89,4200],_?PrimeQ]-1] (* _Harvey P. Dale_, Apr 05 2012 *)
%t Select[Range[0, 100000], PrimeQ[(750*10^# + 51)/9] &] (* _Robert Price_, Oct 20 2015 *)
%o (PARI) a=89;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-51)
%o (PARI) for(n=0,1500,if(isprime((750*10^n+51)/9),print1(n,",")))
%Y Cf. A000533, A002275, A103078.
%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(20) from Erik Branger May 01 2013 by _Ray Chandler_, Apr 29 2015
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