A101837 - OEIS

%I #20 Sep 08 2022 08:45:16

%S 0,2,5,11,32,68,110,1964,5645,7403,11102,20789,24839,38198,90668

%N Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) - 13 for n > 0.

%C Numbers n such that (320*10^n + 13)/9 is prime.

%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 5 followed by digit 7 is prime.

%C a(16) > 10^5. - _Robert Price_, Apr 07 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/3/35557.htm#prime">Prime numbers of the form 355...557</a>.

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

%F a(n) = A102972(n+1) - 1.

%e 3557 is prime, hence 2 is a term.

%t Select[Range[0, 10000], PrimeQ[(320*10^# + 13)/9] &] (* _Robert Price_, Apr 07 2015 *)

%o (PARI) a=37;for(n=0,2000,if(isprime(a),print1(n,","));a=10*a-13)

%o (PARI) for(n=0,2000,if(isprime((320*10^n+13)/9),print1(n,",")))

%o (Magma) [n: n in [0..1000] | IsPrime((320*10^n+13) div 9)]; // _Vincenzo Librandi_, Apr 08 2015

%Y Cf. A000533, A002275, A102972.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

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

%E a(11)-a(15) derived from A102972 by _Robert Price_, Apr 07 2015