cp's OEIS Frontend

A102006 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) - 27 for n > 0.

%I A102006 #19 Jan 17 2019 13:44:06
%S A102006 0,1,4,5,10,16,17,38,55,100,104,106,122,412,425,2606,7667,10469,11020,
%T A102006 17752,26926,60775,98287,300475
%N A102006 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) - 27 for n > 0.
%C A102006 Numbers n such that 10*10^n + 3 is prime.
%C A102006 Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.
%C A102006 Numbers corresponding to terms <= 425 are certified primes.
%C A102006 No other terms <99,999.
%D A102006 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A102006 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/10003.htm#prime">Prime numbers of the form 100...003</a>.
%F A102006 a(n) = A049054(n) - 1.
%e A102006 100003 is prime, hence 4 is a term.
%o A102006 (PARI) a=13;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)
%o A102006 (PARI) for(n=0,1500,if(isprime(10*10^n+3),print1(n,",")))
%Y A102006 Cf. A000533, A002275, A049054, A159352.
%K A102006 nonn,hard,more
%O A102006 1,3
%A A102006 _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
%E A102006 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E A102006 a(22)=60775, a(23)=98287 from _Robert Price_, Mar 03 2011
%E A102006 a(24) from A049054 by _Ray Chandler_, May 01 2015