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Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 61 for n > 0.
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%I #22 Feb 01 2023 21:54:09

%S 0,2,5,50,56,62,149,392,419,546,42023,43062,101612,107384

%N Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 61 for n > 0.

%C Numbers n such that (110*10^n + 61)/9 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 546 are certified primes.

%C a(13) > 10^5. - _Robert Price_, Jan 17 2015

%C a(15) > 2*10^5. - _Tyler Busby_, Feb 01 2023

%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/1/12229.htm#prime">Prime numbers of the form 122...229</a>.

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

%F a(n) = A102931(n) - 1.

%e 1222229 is prime, hence 5 is a term.

%o (PARI) a=19;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-61)

%o (PARI) for(n=0,1500,if(isprime((110*10^n+61)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102931.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

%E a(11)-a(12) derived from A102931 by _Robert Price_, Jan 17 2015

%E a(13)-a(14) from _Tyler Busby_, Jan 31 2023