A101529 - OEIS

%I #16 Jan 17 2019 13:44:06

%S 0,1,4,9,39,46,57,72,91,112,123,129,886,1233,1537,2062,2590,2785,3144,

%T 21687,32380,39169,47790,83877

%N Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 23 for n > 0.

%C Numbers n such that (580*10^n + 23)/9 is prime.

%C Numbers n such that digit 6 followed by n >= 0 occurrences of digit 4 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 886 are certified primes.

%C a(25) > 10^5. - _Robert Price_, Sep 15 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/6/64447.htm#prime">Prime numbers of the form 644...447</a>.

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

%F a(n) = A103036(n) - 1.

%e 647 is prime, hence 1 is a term.

%t Select[Range[0, 100000], PrimeQ[(580*10^# + 23)/9] &] (* _Robert Price_, Sep 15 2015 *)

%o (PARI) a=67;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-23)

%o (PARI) for(n=0,1500,if(isprime((580*10^n+23)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103036.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(20)-a(23) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(24) from _Robert Price_, Sep 15 2015