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Indices of primes in sequence defined by A(0) = 57, A(n) = 10*A(n-1) + 17 for n > 0.
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%I #20 Sep 08 2022 08:45:16

%S 1,5,7,19,107,287,305,461,20101,30041,69049

%N Indices of primes in sequence defined by A(0) = 57, A(n) = 10*A(n-1) + 17 for n > 0.

%C Numbers n such that (530*10^n - 17)/9 is prime.

%C Numbers n such that digit 5 followed by n >= 0 occurrences of digit 8 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 461 are certified primes.

%C a(12) > 10^5. - _Robert Price_, Sep 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/5/58887.htm#prime">Prime numbers of the form 588...887</a>.

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

%F a(n) = A103023(n) - 1.

%e 587 is prime, hence 1 is a term.

%t Select[Range[0, 300], PrimeQ[(530*10^# - 17)/9] &] (* _Robert Price_, Sep 07 2015 *)

%o (PARI) a=57;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+17)

%o (PARI) for(n=0,1000,if(isprime((530*10^n-17)/9),print1(n,",")))

%o (Magma) [n: n in [0..350] | IsPrime((530*10^n-17) div 9 )]; // _Vincenzo Librandi_, Sep 08 2015

%Y Cf. A000533, A002275, A103023.

%K nonn,more

%O 1,2

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

%E a(9)-a(10) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(11) from _Robert Price_, Sep 07 2015