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 A101718 Indices of primes in sequence defined by A(0) = 49, A(n) = 10*A(n-1) - 71 for n > 0. 1

%I

%S 1,4,76,205,1870,3886,11581,20233,60289

%N Indices of primes in sequence defined by A(0) = 49, A(n) = 10*A(n-1) - 71 for n > 0.

%C Numbers n such that (370*10^n + 71)/9 is prime.

%C Numbers n such that digit 4 followed by n >= 0 occurrences of digit 1 followed by digit 9 is prime.

%C a(10) > 10^5. - _Robert Price_, Apr 14 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/4/41119.htm#prime">Prime numbers of the form 411...119</a>.

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

%F a(n) = A102983(n) - 1.

%e 411119 is prime, hence 4 is a term.

%t Select[Range[0, 2000], PrimeQ[(370*10^# + 71)/9] &] (* _Robert Price_, Apr 14 2015 *)

%o (PARI) a=49;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-71)

%o (PARI) for(n=0,1500,if(isprime((370*10^n+71)/9),print1(n,",")))

%o (MAGMA) [n: n in [0..300] | IsPrime((370*10^n+71) div 9)]; // _Vincenzo Librandi_, Apr 15 2015

%Y Cf. A000533, A002275, A102983.

%K nonn,hard,more

%O 1,2

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

%E 3886 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(7)-a(9) derived from A102983 by _Robert Price_, Apr 14 2015

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)