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Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 33 for n > 0.
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%I #15 Jan 17 2019 13:44:06

%S 0,1,2,3,5,6,7,11,22,58,74,143,203,267,759,1215,1429,1505,1508,2803,

%T 2923,3200,3304,5752,9267,11278,19676,23413,28626,31361,42298,49118,

%U 63746,81766

%N Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 33 for n > 0.

%C Numbers n such that (420*10^n - 33)/9 is prime.

%C Numbers n such that digit 4 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 759 are certified primes.

%C a(35) > 10^5. - _Robert Price_, Mar 30 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/4/46663.htm#prime">Prime numbers of the form 466...663</a>.

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

%F a(n) = A099005(n) - 1.

%e 463 is prime, hence 1 is a term.

%t Select[Range[0, 100], PrimeQ[(420*10^# - 33)/9] &]

%o (PARI) a=43;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+33)

%o (PARI) for(n=0,1500,if(isprime((420*10^n-33)/9),print1(n,",")))

%Y Cf. A000533, A002275, A099005.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(28)-a(34) derived from A099005 by _Robert Price_, Mar 30 2015