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Indices of primes in sequence defined by A(0) = 29, A(n) = 10*A(n-1) - 81 for n > 0.
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%I #26 Jan 17 2019 13:44:06

%S 0,4,24,454,760,9204,13560,15954,26668,113940

%N Indices of primes in sequence defined by A(0) = 29, A(n) = 10*A(n-1) - 81 for n > 0.

%C Numbers n such that 20*10^n + 9 is prime.

%C Numbers n such that digit 2 followed by n >= 0 occurrences of digit 0 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 760 are certified primes.

%C a(11) > 2*10^5. - _Robert Price_, Jun 06 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/2/20009.htm#prime">Prime numbers of the form 200...009</a>.

%F a(n) = A101392(n-1) - 1. - _Robert Price_, Nov 25 2014

%e 200009 is prime, hence 4 is a term.

%t Select[Range[0, 300], PrimeQ[20*10^# + 9] &] (* _Robert Price_, Jun 06 2015 *)

%o (PARI) a=29;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-81)

%o (PARI) for(n=0,1500,if(isprime(20*10^n+9),print1(n,",")))

%Y Cf. A000533, A002275, A101392.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(9)-a(10) derived from A101392 by _Robert Price_, Nov 25 2014