A102019 - OEIS

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

%S 0,2,5,14,69,75,13023,60345

%N Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) + 23 for n > 0.

%C Numbers n such that (140*10^n - 23)/9 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 75 are certified primes.

%C a(9) > 10^5. - Robert Price, Apr 10 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/1/15553.htm#prime">Prime numbers of the form 155...553</a>.

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

%F a(n) = A102936(n) - 1.

%e 1553 is prime, hence 2 is a term.

%t Flatten[Position[NestList[10#+23&,13,75],_?PrimeQ]]-1 (* _Harvey P. Dale_, Jul 21 2013 *)

%t Select[Range[0, 10000], PrimeQ[(140*10^# - 23)/9] &] (* _Robert Price, Apr 10 2015 *)

%o (PARI) a=13;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+23)

%o (PARI) for(n=0,1500,if(isprime((140*10^n-23)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102936.

%K nonn,hard,more

%O 1,2

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

%E a(7)-a(8) derived from A102936 by _Robert Price_, Apr 10 2015