A102033 - OEIS

%I #26 Jan 17 2019 13:44:07

%S 0,1,2,3,5,15,20,27,47,81,121,129,281,303,4601,12983,13613,42760,

%T 90595,109927,158241

%N Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) + 63 for n > 0.

%C Numbers n such that (180*10^n - 63)/9 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 303 are certified primes.

%C a(20) > 10^5. - _Robert Price_, Nov 16 2014

%C a(22) > 2*10^5. - _Robert Price_, Oct 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/1/19993.htm#prime">Prime numbers of the form 199...993</a>.

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

%F a(n) = A102946(n) - 1. - _Robert Price_, Nov 16 2014

%e 193 is prime, hence 1 is a term.

%p A102033:=n->`if`(isprime((180*10^n-63)/9), n, NULL): seq(A102033(n), n=0..10^3); # _Wesley Ivan Hurt_, Nov 16 2014

%t Select[Range[0, 10^3], PrimeQ[(180*10^# - 63)/9] &] (* _Wesley Ivan Hurt_, Nov 16 2014 *)

%o (PARI) a=13;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+63)

%o (PARI) for(n=0,1500,if(isprime((180*10^n-63)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102946.

%K nonn,hard,more

%O 1,3

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

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(18)-a(19) derived from A102946 by _Robert Price_, Nov 16 2014

%E a(20)-a(21) from _Robert Price_, Oct 25 2015