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A101532 Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) + 23 for n > 0. 1

%I

%S 1,2,8,10,11,14,35,37,40,76,89,95,131,373,398,616,1331,1394,1810,2803,

%T 4952,5309,16675,29335

%N Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) + 23 for n > 0.

%C Numbers n such that (590*10^n - 23)/9 is prime.

%C Numbers n such that digit 6 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 616 are certified primes.

%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/6/65553.htm#prime">Prime numbers of the form 655...553</a>.

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

%F a(n) = A103039(n) - 1.

%e 6553 is prime, hence 2 is a term.

%t Flatten[Position[NestList[10#+23&,63,1900],_?PrimeQ]]-1 (* To generate more terms, change the constant 1900 to a larger number, but computation times will increase rapidly. *) (* _Harvey P. Dale_, May 06 2013 *)

%o (PARI) a=63;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+23)

%o (PARI) for(n=0,1500,if(isprime((590*10^n-23)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103039.

%K nonn,hard,more

%O 1,2

%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(23)-a(24) from Kamada data by _Ray Chandler_, Apr 30 2015

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)