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Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 63 for n > 0.
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%I #16 Jan 17 2019 13:44:06

%S 0,2,4,5,9,11,12,38,47,53,63,81,146,147,359,398,1637,1875,2145,2193,

%T 15788,23073,38465,68399

%N Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 63 for n > 0.

%C Numbers n such that (720*10^n - 63)/9 is prime.

%C Numbers n such that digit 7 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 398 are certified primes.

%C a(25) > 2*10^5. - _Robert Price_, Nov 11 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/7/79993.htm#prime">Prime numbers of the form 799...993</a>.

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

%F a(n) = A099190(n) - 1.

%e 7999993 is prime, hence 5 is a term.

%t Select[Range[0, 100000], PrimeQ[(720*10^# - 63)/9] &] (* _Robert Price_, Nov 11 2015 *)

%o (PARI) a=73;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+63)

%o (PARI) for(n=0,1000,if(isprime((720*10^n-63)/9),print1(n,",")))

%Y Cf. A000533, A002275, A101849, A169830, A099190.

%K nonn,hard,more

%O 1,2

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

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

%E a(21)-a(24) from Kamada data by _Ray Chandler_, Apr 30 2015