A101728 - OEIS

%I #15 Jan 17 2019 13:44:06

%S 5,20,21,23,50,80,131,164,620,1449,3423,5978,11525,26979,49232,84926

%N Indices of primes in sequence defined by A(0) = 49, A(n) = 10*A(n-1) - 31 for n > 0.

%C Numbers n such that (410*10^n + 31)/9 is prime.

%C Numbers n such that digit 4 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 620 are certified primes.

%C a(17) > 10^5. - _Robert Price_, May 25 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/4/45559.htm#prime">Prime numbers of the form 455...559</a>.

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

%F a(n) = A102993(n) - 1.

%e 4555559 is prime, hence 5 is a term.

%t Select[Range[0, 1000], PrimeQ[(410*10^# + 31)/9] &] (* _Robert Price_, May 25 2015 *)

%o (PARI) a=49;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-31)

%o (PARI) for(n=0,1500,if(isprime((410*10^n+31)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102993.

%K nonn,hard,more

%O 1,1

%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 02 2008

%E a(13)-a(15) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(16) from _Robert Price_, May 25 2015