login
Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 3 for n > 0.
1

%I #22 Sep 08 2022 08:45:16

%S 0,1,5,9,11,12,21,31,45,60,67,89,109,651,1607,1903,2002,3037,3085,

%T 9579,9697,10638,14460

%N Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 3 for n > 0.

%C Numbers n such that (420*10^n + 3)/9 is prime.

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

%C Numbers corresponding to terms <= 651 are certified primes.

%C a(24) > 2*10^5. - _Robert Price_, Jul 11 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/4/46667.htm#prime">Prime numbers of the form 466...667</a>.

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

%F a(n) = A099017(n+1) - 1.

%e 467 is prime, hence 1 is a term.

%t Select[Range[0, 100], PrimeQ[(420 10^# + 3)/9] &] (* _Vincenzo Librandi_, Jul 12 2015 *)

%o (PARI) a=47;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-3)

%o (PARI) for(n=0,1500,if(isprime((420*10^n+3)/9),print1(n,",")))

%o (Magma) [n: n in [0..500] | IsPrime((420*10^n+3) div 9)]; // _Vincenzo Librandi_, Jul 12 2015

%Y Cf. A000533, A002275, A099017.

%K nonn,hard,more

%O 1,3

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