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Indices of primes in sequence defined by A(0) = 91, A(n) = 10*A(n-1) + 61 for n > 0.
1

%I #24 Jan 17 2019 13:44:06

%S 1,3,40,52,63,196,237,783,3913,4435,12537,19035

%N Indices of primes in sequence defined by A(0) = 91, A(n) = 10*A(n-1) + 61 for n > 0.

%C Numbers n such that (880*10^n - 61)/9 is prime.

%C Numbers n such that digit 9 followed by n >= 0 occurrences of digit 7 followed by digit 1 is prime.

%C Numbers corresponding to terms <= 783 are certified primes.

%C a(13) > 10^5. - _Robert Price_, Nov 10 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/9/97771.htm#prime">Prime numbers of the form 977...771</a>.

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

%F a(n) = A103105(n+1) - 1.

%e 97771 is prime, hence 3 is a term.

%t Select[Range[500],PrimeQ[(880*10^#-61)/9]&] (* _Harvey P. Dale_, Jul 19 2011 *)

%o (PARI) a=91;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+61)

%o (PARI) for(n=0,1000,if(isprime((880*10^n-61)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103105.

%K nonn,hard,more

%O 1,2

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

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

%E a(11)-a(12) from Kamada data by _Ray Chandler_, Apr 28 2015