A056247 - OEIS

%I #24 Jan 17 2019 13:44:05

%S 0,3,11,15,17,35,51,71,99,6231,24027,40221,66393

%N Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 51 for n > 0.

%C Numbers n such that (150*10^n - 51)/9 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 6 followed by digit 1 is prime.

%C Numbers corresponding to terms <= 99 are certified primes.

%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#pdp161">PDP Reference Table - 161</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/16661.htm#prime">Prime numbers of the form 166...661</a>.

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

%F a(n) = A082700(n-1) - 2 for n > 1.

%e 16661 is prime, hence 3 is a term.

%t Select[Range[0, 2000], PrimeQ[(150 10^# - 51) / 9] &] (* _Vincenzo Librandi_, Nov 03 2014 *)

%o (PARI) a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+51)

%o (PARI) for(n=0,1500,if(isprime((150*10^n-51)/9),print1(n,",")))

%Y Cf. A000533, A002275, A068647, A082700.

%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 28 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 Added one more term from the PDP table and a link, by _Patrick De Geest_, Nov 02 2014

%E Edited by _Ray Chandler_, Nov 04 2014