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%I #26 Sep 08 2022 08:45:16
%S 0,5,8,14,23,47,72,74,96,248,272,2487,14498,74772,87448
%N Indices of primes in sequence defined by A(0) = 31, A(n) = 10*A(n-1) + 41 for n > 0.
%C Numbers n such that (320*10^n - 41)/9 is prime.
%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 5 followed by digit 1 is prime.
%C Numbers corresponding to terms <= 272 are certified primes.
%C a(16) > 10^5. - _Robert Price_, May 24 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/3/35551.htm#prime">Prime numbers of the form 355...551</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A102971(n) - 1.
%e 3555555551 is prime, hence 8 is a term.
%t #-1&/@Flatten[Position[NestList[10#+41&,31,280],_?PrimeQ]] (* _Harvey P. Dale_, Jul 17 2011 *)
%t Select[Range[0, 10000], PrimeQ[(320 10^# - 41)/9] &] (* _Vincenzo Librandi_, May 25 2015 *)
%o (PARI) a=31;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+41)
%o (PARI) for(n=0,1500,if(isprime((320*10^n-41)/9),print1(n,",")))
%o (Magma) [n: n in [0..2000] | IsPrime((320*10^n-41) div 9)]; // _Vincenzo Librandi_, May 26 2015
%Y Cf. A000533, A002275, A102971.
%K nonn,hard,more
%O 1,2
%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004
%E 2487 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E a(13) from Kamada data by _Ray Chandler_, May 01 2015
%E a(14)-a(15) from _Robert Price_, May 24 2015
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