|
%I #32 Feb 01 2023 19:57:16
%S 1,11,13,29,103,125,341,599,9823
%N Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 17 for n > 0.
%C Numbers n such that (280*10^n + 17)/9 is prime.
%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.
%C Numbers corresponding to terms <= 599 are certified primes.
%C All terms are odd since 11 is the only palindromic prime with an even number of digits. - _Chai Wah Wu_, Nov 05 2019
%C a(10) > 2*10^5. - _Tyler Busby_, Feb 01 2023
%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#pdp313">PDP Reference Table - 313</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/31113.htm#prime">Prime numbers of the form 311...113</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A082704(n) - 2.
%e 313 is prime, hence 1 is a term.
%t Flatten[Position[NestList[10#-17&,33,600],_?PrimeQ]-1] (* This generates the first 8 terms of the sequence. Changing the last constant from 600 to 9825 will generate all 9 terms of the sequence but it will take a long time to do so. - _Harvey P. Dale_, May 16 2012 *)
%t Select[Range[0, 2000], PrimeQ[(280 10^# + 17) / 9] &] (* _Vincenzo Librandi_, Nov 03 2014 *)
%o (PARI) a=33;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-17)
%o (PARI) for(n=0,1500,if(isprime((280*10^n+17)/9),print1(n,",")))
%Y Cf. A000533, A002275, A068650, A082704.
%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_ at the suggestion of _Andrew S. Plewe_, Jun 15 2007
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E Added and updated the links section, by _Patrick De Geest_, Nov 02 2014
%E Edited by _Ray Chandler_, Nov 04 2014
| 