cp's OEIS Frontend

A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.

%I A101951 #26 Sep 08 2022 08:45:16
%S A101951 0,2,4,5,6,11,15,16,21,23,34,114,119,357,1487,1818,4678,9820,27216,
%T A101951 27692,194412
%N A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.
%C A101951 Numbers n such that 20*10^n + 3 is prime.
%C A101951 Numbers n such that digit 2 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.
%C A101951 Numbers corresponding to terms <= 357 are certified primes.
%C A101951 a(21) > 10^5. - _Robert Price_, Nov 16 2014
%C A101951 a(22) > 2*10^5. - Robert Price, Jul 11 2015
%D A101951 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A101951 Makoto Kamada, <a href="https://stdkmd.net/nrr/2/20003.htm#prime">Prime numbers of the form 200...003</a>.
%F A101951 a(n) = A081677(n+1) - 1. - _Robert Price_, Nov 16 2014
%e A101951 2003 is prime, hence 2 is a term.
%t A101951 Select[Range[0, 1000], PrimeQ[(20 10^# + 3)] &] (* _Vincenzo Librandi_, Nov 17 2014 *)
%o A101951 (PARI) a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)
%o A101951 (PARI) for(n=0,1500,if(isprime(20*10^n+3),print1(n,",")))
%o A101951 (Magma) [n: n in [0..500] | IsPrime(20*10^n+3)]; // _Vincenzo Librandi_, Nov 17 2014
%Y A101951 Cf. A000533, A002275, A081677.
%K A101951 nonn,hard,more
%O A101951 1,2
%A A101951 _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004
%E A101951 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E A101951 a(19)-a(20) derived from A081677 by _Robert Price_, Nov 16 2014
%E A101951 a(21) from _Robert Price_, Jul 11 2015