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 A101720 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) - 7 for n > 0. 1

%I

%S 0,3,8,9,30,69,159,170,276,629,723,3716,5541,5633,10655,12723,31953

%N Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) - 7 for n > 0.

%C Numbers n such that (380*10^n + 7)/9 is prime.

%C Numbers n such that digit 4 followed by n >= 0 occurrences of digit 2 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 723 are certified primes.

%C a(18) > 10^5. - _Robert Price_, May 09 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/4/42223.htm#prime">Prime numbers of the form 422...223</a>.

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

%F a(n) = A102985(n+1) - 1.

%e 42223 is prime, hence 3 is a term.

%t Select[Range[0, 300], PrimeQ[(380*10^# + 7)/ 9] &] (* _Robert Price_, May 09 2015 *)

%o (PARI) a=43;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-7)

%o (PARI) for(n=0,1500,if(isprime((380*10^n+7)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102985.

%K nonn,hard,more

%O 1,2

%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(15)-a(17) from Kamada data by _Ray Chandler_, Apr 30 2015

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Last modified September 30 21:27 EDT 2020. Contains 337440 sequences. (Running on oeis4.)