|
%I #16 Jan 17 2019 13:44:06
%S 0,3,9,11,12,39,75,122,500,647,3540,4001,4227,5270,7431,27305,43401
%N Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 53 for n > 0.
%C Numbers n such that (440*10^n - 53)/9 is prime.
%C Numbers n such that digit 4 followed by n >= 0 occurrences of digit 8 followed by digit 3 is prime.
%C Numbers corresponding to terms <= 647 are certified primes.
%C a(18) > 10^5. - _Robert Price_, Jun 01 2015
%D Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/4/48883.htm#prime">Prime numbers of the form 488...883</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A102998(n) - 1.
%e 48883 is prime, hence 3 is a term.
%t Select[Range[0, 1000], PrimeQ[(440*10^# - 53)/9] &] (* _Robert Price_, Jun 01 2015 *)
%o (PARI) a=43;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+53)
%o (PARI) for(n=0,1500,if(isprime((440*10^n-53)/9),print1(n,",")))
%Y Cf. A000533, A002275, A102998.
%K nonn,hard,more
%O 1,2
%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E a(16)-a(17) from Kamada data by _Ray Chandler_, May 01 2015
|
