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A101726 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 23 for n > 0. 1

%I

%S 0,3,6,18,33,53,77,89,212,306,701,1455,2138,2213,3065,9299,16439,

%T 16893,28574,54050

%N Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 23 for n > 0.

%C Numbers n such that (410*10^n - 23)/9 is prime.

%C Numbers n such that digit 4 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 701 are certified primes.

%C a(21) > 10^5. _Robert Price_, May 08 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/4/45553.htm#prime">Prime numbers of the form 455...553</a>.

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

%F a(n) = A102991(n+1) - 1.

%e 45553 is prime, hence 3 is a term.

%t Select[Range[0, 300], PrimeQ[(410*10^# - 23)/9] &] (* _Robert Price_, May 08 2015 *)

%o (PARI) a=43;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+23)

%o (PARI) for(n=0,1500,if(isprime((410*10^n-23)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102991.

%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 02 2008

%E a(17)-a(19) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(20) from _Robert Price_, May 08 2015

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Last modified July 21 19:22 EDT 2019. Contains 325199 sequences. (Running on oeis4.)