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Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) + 63 for n > 0.
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%I #15 Jan 17 2019 13:44:06

%S 0,1,4,5,6,10,16,28,41,46,95,107,165,209,330,1021,3592,4425,5703,

%T 13935,16485,85909

%N Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) + 63 for n > 0.

%C Numbers n such that (540*10^n - 63)/9 is prime.

%C Numbers n such that digit 5 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 330 are certified primes.

%C a(23) > 2*10^5. - Robert Price, Aug 07 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/5/59993.htm#prime">Prime numbers of the form 599...993</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A103025(n) - 1.

%e 593 is prime, hence 1 is a term.

%t Select[Range[0, 200000], PrimeQ[(540*10^# - 63)/9] &] (* _Robert Price_, Aug 07 2015 *)

%o (PARI) a=53;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+63)

%o (PARI) for(n=0,1500,if(isprime((540*10^n-63)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103025.

%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(20)-a(22) from Kamada data by _Ray Chandler_, Apr 30 2015