A101002 - OEIS

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

%S 4,28,59,146,185,455,677,1372,3377,15725,68230

%N Indices of primes in sequence defined by A(0) = 93, A(n) = 10*A(n-1) - 7 for n > 0.

%C Numbers n such that (830*10^n + 7)/9 is prime.

%C Numbers n such that digit 9 followed by n >= 0 occurrences of digit 2 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 677 are certified primes.

%C a(12) > 10^5. - _Robert Price_, Oct 31 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/9/92223.htm#prime">Prime numbers of the form 922...223</a>.

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

%F a(n) = A103094(n) - 1.

%e 922223 is prime, hence 4 is a term.

%t Select[Range[0, 300], PrimeQ[(830*10^# + 7)/9] &] (* _Robert Price_, Oct 31 2015 *)

%o (PARI) a=93;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-7)

%o (PARI) for(n=0,1500,if(isprime((830*10^n+7)/9 ),print1(n,",")))

%Y Cf. A000533, A002275, A103094.

%K nonn,hard,more,less

%O 1,1

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

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

%E a(10) from Kamada data by _Ray Chandler_, Apr 28 2015

%E a(11) from _Robert Price_, Oct 31 2015