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A101129 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) - 27 for n > 0.

%I A101129 #25 Sep 08 2022 08:45:16
%S A101129 0,3,5,15,21,38,102,162,239,1047,1973,2558,5879,14435,28337,32795,
%T A101129 38078,56778,91214,111324,115862,138603
%N A101129 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) - 27 for n > 0.
%C A101129 Numbers n such that 70*10^n + 3 is prime.
%C A101129 Numbers n such that digit 7 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.
%C A101129 Numbers corresponding to terms <= 239 are certified primes.
%C A101129 Certified primality of number corresponding to term 1047 with Primo. - _Ryan Propper_, Jun 20 2005
%C A101129 a(23) > 2*10^5. - _Robert Price_, Aug 15 2015
%D A101129 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A101129 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/70003.htm#prime">Prime numbers of the form 700...003</a>.
%H A101129 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F A101129 a(n) = A097970(n) - 1.
%e A101129 7000003 is prime, hence 5 is a term.
%t A101129 Select[Range[0, 200000], PrimeQ[70*10^# + 3] &] (* _Robert Price_, Aug 15 2015 *)
%o A101129 (PARI) a=73;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)
%o A101129 (PARI) for(n=0,1500,if(isprime(70*10^n+3),print1(n,",")))
%o A101129 (Magma) [n: n in [0..500] | IsPrime(70*10^n + 3)]; // _Vincenzo Librandi_, Aug 16 2015
%Y A101129 Cf. A000533, A002275, A097970.
%K A101129 nonn,hard,more
%O A101129 1,2
%A A101129 _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004
%E A101129 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E A101129 a(14)-a(19) from Kamada data by _Ray Chandler_, Apr 29 2015
%E A101129 a(20)-a(22) from _Robert Price_, Aug 15 2015