cp's OEIS Frontend

A056245 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0.

%I A056245 #32 Aug 15 2024 03:35:01
%S A056245 0,5,65,1253,8405,67037
%N A056245 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0.
%C A056245 Numbers n such that (130*10^n - 31)/9 is prime.
%C A056245 Numbers n such that digit 1 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.
%C A056245 Numbers corresponding to terms <= 1253 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.
%C A056245 a(7) > 2*10^5. - _Tyler Busby_, Feb 01 2023
%D A056245 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A056245 Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp141">PDP Reference Table - 141</a>.
%H A056245 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/14441.htm#prime">Prime numbers of the form 144...441</a>.
%H A056245 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F A056245 a(n) = A082698(n-1) - 2 for n > 1.
%e A056245 1444441 is prime, hence 5 is a term.
%t A056245 Select[Range[0, 2000], PrimeQ[(130 10^# - 31) / 9] &] (* _Vincenzo Librandi_, Nov 03 2014 *)
%o A056245 (PARI) a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+31)
%o A056245 (PARI) for(n=0,1500,if(isprime((130*10^n-31)/9),print1(n,",")))
%o A056245 (Magma) [n: n in [0..500] | IsPrime((130*10^n-31) div 9)]; // _Vincenzo Librandi_, Nov 03 2014
%Y A056245 Cf. A000533, A002275, A082698.
%K A056245 nonn,hard,more
%O A056245 1,2
%A A056245 _Robert G. Wilson v_, Aug 18 2000
%E A056245 Additional comments from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
%E A056245 Edited by _N. J. A. Sloane_, Jun 15 2007
%E A056245 8405 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E A056245 Added one more term from the PDP table and updated a link, by _Patrick De Geest_, Nov 02 2014
%E A056245 Edited by _Ray Chandler_, Nov 04 2014