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Indices of primes in sequence defined by A(0) = 71, A(n) = 10*A(n-1) + 81 for n > 0.
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%I #17 Jan 17 2019 13:44:06

%S 0,4,10,11,16,27,45,47,60,72,137,177,212,404,761,1052,1156,1426,2864,

%T 3147,3614,13446,48080

%N Indices of primes in sequence defined by A(0) = 71, A(n) = 10*A(n-1) + 81 for n > 0.

%C Numbers n such that (720*10^n - 81)/9 is prime.

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

%C Numbers corresponding to terms <= 761 are certified primes.

%C a(24) > 2*10^5. - _Robert Price_, Dec 19 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/7/79991.htm#prime">Prime numbers of the form 799...991</a>.

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

%F a(n) = A103068(n) - 1.

%e 799991 is prime, hence 4 is a term.

%t Select[Range[0, 300], PrimeQ[(720*10^# - 81)/9] &] (* _Robert Price_, Dec 19 2015 *)

%o (PARI) a=71;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+81)

%o (PARI) for(n=0,1500,if(isprime((720*10^n-81)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103068.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

%E a(19) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Apr 13 2006

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

%E a(22)-a(23) from Kamada data by _Ray Chandler_, Apr 30 2015