A101064 - OEIS

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

%S 0,1,4,7,13,54,102,330,1066,13710,24396,54582

%N Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 61 for n > 0.

%C Numbers n such that (740*10^n + 61)/9 is prime.

%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 1066 are certified primes.

%C a(13) > 10^5. - _Robert Price_, Oct 26 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/8/82229.htm#prime">Prime numbers of the form 822...229</a>.

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

%F a(n) = A103077(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%e 822229 is prime, hence 4 is a term.

%t Flatten[Position[NestList[10#-61&,89,1100],_?PrimeQ]]-1 (* _Harvey P. Dale_, Aug 16 2014 *)

%t Select[Range[0, 100000], PrimeQ[(740*10^# + 61)/9] &] (* _Robert Price_, Oct 26 2015 *)

%o (PARI) a=89;for(n=0,1200,if(isprime(a),print1(n,","));a=10*a-61)

%o (PARI) for(n=0,1200,if(isprime((740*10^n+61)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103077.

%K nonn,hard,more

%O 1,3

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

%E a(10)-a(11) from Kamada data by _Ray Chandler_, Apr 29 2015

%E a(12) from _Robert Price_, Oct 26 2015