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Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) + 33 for n > 0.
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%I #16 Apr 16 2024 16:12:31

%S 0,1,2,17,176,323,387,391,403,530,1082,12545,22442,54387,72915,185519

%N Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) + 33 for n > 0.

%C Numbers n such that (150*10^n - 33)/9 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 530 are certified primes.

%C a(16) > 10^5. - _Robert Price_, Nov 15 2014

%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/1/16663.htm#prime">Prime numbers of the form 166...663</a>.

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

%F a(n) = A102939(n) - 1. - _Robert Price_, Nov 15 2014

%e 163 is prime, hence 1 is a term.

%o (PARI) a=13;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+33)

%o (PARI) for(n=0,1500,if(isprime((150*10^n-33)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102939.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

%E a(12)-a(15) derived from A102939 by _Robert Price_, Nov 15 2014

%E a(16) derived from A102939 by _Tyler Busby_, Apr 16 2024