A101579 - OEIS

%I #13 Jan 17 2019 13:44:06

%S 0,2,3,8,11,59,267,288,383,794,3473,9179,76437

%N Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) + 13 for n > 0.

%C Numbers n such that (490*10^n - 13)/9 is prime.

%C Numbers n such that digit 5 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 794 are certified primes.

%C a(14) > 10^5. - Robert Price, Jul 16 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/5/54443.htm#prime">Prime numbers of the form 544...443</a>.

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

%F a(n) = A103014(n) - 1.

%e 54443 is prime, hence 3 is a term.

%t Select[Range[0,100000],PrimeQ[(490*10^#-13)/9]&]

%o (PARI) a=53;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+13)

%o (PARI) for(n=0,1000,if(isprime((490*10^n-13)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103014.

%K nonn,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(13) from _Robert Price_, Jul 16 2015