A101056 - OEIS

%I #15 Jan 17 2019 13:44:06

%S 0,30,104,112,368,1358,6218,105570,150974

%N Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) - 27 for n > 0.

%C Numbers n such that 80*10^n + 3 is prime.

%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 368 are certified primes.

%C a(10) > 2*10^5. - _Robert Price_ Aug 19 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/8/80003.htm#prime">Prime numbers of the form 800...003</a>.

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

%F a(n) = A103069(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%e 83 is prime, hence 0 is a term.

%t Select[Range[0, 20000], PrimeQ[80*10^# + 3] &] (* _Robert Price_, Aug 19 2015 *)

%o (PARI) a=83;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

%o (PARI) for(n=0,1500,if(isprime(80*10^n+3),print1(n,",")))

%Y Cf. A000533, A002275, A103069.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

%E 6218 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(8) - a(9) from _Robert Price_, Aug 19 2015