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Indices of primes in sequence defined by A(0) = 59, A(n) = 10*A(n-1) - 81 for n > 0.
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%I #19 Jan 17 2019 13:44:06

%S 0,1,2,4,7,19,28,85,282,756,1198,2472,2732,24852,39628,53491,71236,

%T 72301,81652,167509

%N Indices of primes in sequence defined by A(0) = 59, A(n) = 10*A(n-1) - 81 for n > 0.

%C Numbers n such that 50*10^n + 9 is prime.

%C Numbers n such that digit 5 followed by n >= 0 occurrences of digit 0 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 756 are certified primes.

%C a(21) > 2*10^5. - _Robert Price_, Aug 10 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/5/50009.htm#prime">Prime numbers of the form 500...009</a>.

%F a(n) = A103004(n) - 1.

%e 500009 is prime, hence 4 is a term.

%t Select[Range[0, 200000], PrimeQ[50*10^# + 9] &] (* _Robert Price_, Aug 10 2015 *)

%o (PARI) a=59;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-81)

%o (PARI) for(n=0,1500,if(isprime(50*10^n+9),print1(n,",")))

%Y Cf. A000533, A002275, A103004.

%K nonn,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(14)-a(19) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(20) from _Robert Price_, Aug 10 2015