A101148 - OEIS

%I #21 Sep 08 2022 08:45:16

%S 0,6,89,92,124,146,497,867,878,1156,2957,3017,3316,3821,6947,8884,

%T 13091,33322,35846,79491

%N Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 33 for n > 0.

%C Numbers n such that (690*10^n - 33)/9 is prime.

%C Numbers n such that digit 7 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 878 are certified primes.

%C a(21) > 10^5. - _Robert Price_, Oct 14 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/7/76663.htm#prime">Prime numbers of the form 766...663</a>.

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

%F a(n) = A103064(n) - 1.

%e 73 is prime, hence 0 is a term.

%t Select[Range[0, 100000], PrimeQ[(690*10^# - 33)/9] &] (* _Robert Price_, Oct 14 2015 *)

%o (PARI) a=73;for(n=0,1200,if(isprime(a),print1(n,","));a=10*a+33)

%o (PARI) for(n=0,1200,if(isprime((690*10^n-33)/9),print1(n,",")))

%o (Magma) [n: n in [0..500] | IsPrime((690*10^n-33) div 9)]; // _Vincenzo Librandi_, Oct 15 2015

%Y Cf. A000533, A002275, A103064.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

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

%E a(18)-a(19) from Erik Branger May 01 2013 by _Ray Chandler_, Apr 30 2015

%E a(20) from _Robert Price_, Oct 14 2015