A101058 - OEIS

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

%S 0,9,23,198,744,7752,17937,21318,24947,26118,29453,51888,62823,88104

%N Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) - 17 for n > 0.

%C Numbers n such that (730*10^n + 17)/9 is prime.

%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 744 are certified primes.

%C a(15) > 10^5. - _Robert Price_, Oct 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/8/81113.htm#prime">Prime numbers of the form 811...113</a>.

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

%F a(n) = A103071(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%e 81111111113 is prime, hence 9 is a term.

%t Select[Range[0, 100000], PrimeQ[(730*10^# + 17)/9] &] (* _Robert Price_, Oct 16 2015 *)

%o (PARI) a=83;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-17)

%o (PARI) for(n=0,1000,if(isprime((730*10^n+17)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103071.

%K nonn,hard,more

%O 1,2

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

%E 7752 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(7)-a(11) from Kamada data by _Ray Chandler_, Apr 29 2015

%E a(12)-a(14) from _Robert Price_, Oct 16 2015