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Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 13 for n > 0.
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%I #18 Jan 17 2019 13:44:06

%S 0,1,18,30,105,26193,39972

%N Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 13 for n > 0.

%C Numbers n such that (670*10^n - 13)/9 is prime.

%C Numbers n such that digit 7 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 105 are certified primes.

%C The next term, if it exists, is bigger than 4000. - _Stefan Steinerberger_, Feb 04 2006

%C a(8) > 10^5. - _Robert Price_, Sep 25 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/7/74443.htm#prime">Prime numbers of the form 744...443</a>.

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

%F a(n) = A103058(n) - 1.

%e 73 is prime, hence 0 is a term.

%t For[n=0, n < 4000, n++, If[PrimeQ[(670*10^n - 13)/9], Print[n]]] (Steinerberger)

%o (PARI) a=73;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+13)

%o (PARI) for(n=0,1000,if(isprime((670*10^n-13)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103058.

%K nonn,hard

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

%E a(6) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(7) from _Robert Price_, Sep 25 2015