A056256 - OEIS

%I #20 Jan 17 2019 13:44:05

%S 1,11,29,59,115,289,631,1063,1493,5431,7361

%N Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) + 53 for n > 0.

%C Numbers n such that (350*10^n - 53)/9 is prime.

%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 8 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 1493 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

%D Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp383">PDP Reference Table - 383</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/38883.htm#prime">Prime numbers of the form 388...883</a>.

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

%F a(n) = A082709(n) - 2.

%e 383 is prime, hence 1 is a term.

%t Select[Range[0, 2000], PrimeQ[(350 10^# - 53) / 9] &] (* _Vincenzo Librandi_, Nov 03 20124 *)

%o (PARI) a=33;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+53)

%o (PARI) for(n=0,1500,if(isprime((350*10^n-53)/9),print1(n,",")))

%Y Cf. A000533, A002275, A082709.

%K nonn,hard,more

%O 1,2

%A _Robert G. Wilson v_, Aug 18 2000

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

%E Edited by _N. J. A. Sloane_, Jun 15 2007

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

%E Comments section and a link updated by _Patrick De Geest_, Nov 02 2014

%E Edited by _Ray Chandler_, Nov 05 2014