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Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 41 for n > 0.
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%I #16 Jan 17 2019 13:44:06

%S 0,3,12,36,45,105,138,468,5694,56280,58669

%N Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 41 for n > 0.

%C Numbers n such that (760*10^n + 41)/9 is prime.

%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 4 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 468 are certified primes.

%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/8/84449.htm#prime">Prime numbers of the form 844...449</a>.

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

%F a(n) = A103082(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%e 84449 is prime, hence 3 is a term.

%t Select[Range[0,5700],PrimeQ[FromDigits[Join[PadRight[{8},#+1,4],{9}]]]&] (* _Harvey P. Dale_, Jan 23 2012 *)

%o (PARI) a=89;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-41)

%o (PARI) for(n=0,1000,if(isprime((760*10^n+41)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103082.

%K nonn,hard,more

%O 1,2

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

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

%E a(10)-a(11) from _Robert Price_, Oct 18 2015