A101010 - OEIS

%I #16 Jan 17 2019 13:44:06

%S 1,19,103,328,1441,1720,24886

%N Indices of primes in sequence defined by A(0) = 93, A(n) = 10*A(n-1) + 23 for n > 0.

%C Numbers n such that (860*10^n - 23)/9 is prime.

%C Numbers n such that digit 9 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 328 are certified primes.

%C a(8) > 10^5. - _Robert Price_, Nov 08 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/9/95553.htm#prime">Prime numbers of the form 955...553</a>.

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

%F a(n) = A103101(n+1) - 1.

%e 953 is prime, hence 1 is a term.

%t Select[Range[0, 100000], PrimeQ[(860*10^# - 23)/9] &] (* _Robert Price_, Nov 08 2015 *)

%o (PARI) a=93;for(n=0,2000,if(isprime(a),print1(n,","));a=10*a+23)

%o (PARI) for(n=0,2000,if(isprime((860*10^n-23)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103101.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

%E a(7) from Kamada data by _Ray Chandler_, Apr 28 2015