|
%I #27 Jan 17 2019 13:44:05
%S 0,1,3,5,93,159,359,1469,2897,3093,3111,15697,17955,42261,111031
%N Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 21 for n > 0.
%C Numbers n such that (120*10^n - 21)/9 is prime.
%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 3 followed by digit 1 is prime.
%C Numbers corresponding to terms <= 3111 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#pdp131">PDP Reference Table - 131</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/13331.htm#prime">Prime numbers of the form 133...331</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A082697(n-1) - 2 for n > 1.
%e 131 is prime, hence 1 is a term.
%t Do[If[PrimeQ[(1*10^n + 3*(10^n - 1)/9)*10 + 1], Print[n]], {n, 1, 2500}]
%t Select[Range[0, 2000], PrimeQ[(120 10^# - 21) / 9] &] (* _Vincenzo Librandi_, Nov 03 2014 *)
%o (PARI) a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+21)
%o (PARI) for(n=0,1500,if(isprime((120*10^n-21)/9),print1(n,",")))
%Y Cf. A000533, A002275, A068645, A082697.
%K nonn,hard,more
%O 1,3
%A _Robert G. Wilson v_, Aug 18 2000
%E More terms and additional comments from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
%E Edited by _N. J. A. Sloane_, Jun 15 2007
%E Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E a(15)=111031 from _Ray Chandler_, Apr 14 2011
%E Updated comments section and a link, by _Patrick De Geest_, Nov 02 2014
%E Edited by _Ray Chandler_, Nov 04 2014
| 