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Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 33 for n > 0.
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%I #24 Jul 13 2023 12:25:43

%S 0,1,2,4,5,6,10,20,29,67,72,168,175,344,822,1020,1190,2072,2754,10716,

%T 14672,16753,17605,81028,120850,167964,200407

%N Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 33 for n > 0.

%C Numbers n such that (240*10^n - 33)/9 is prime.

%C Numbers n such that digit 2 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 822 are certified primes.

%C a(28) > 3*10^5. - _Robert Price_, Jul 13 2023

%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/2/26663.htm#prime">Prime numbers of the form 266...663</a>.

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

%F a(n) = A098959(n) - 1.

%e 263 is prime, hence 1 is a term.

%o (PARI) a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+33)

%o (PARI) for(n=0,1500,if(isprime((240*10^n-33)/9),print1(n,",")))

%Y Cf. A000533, A002275, A098959.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(24) derived from A098959 by _Robert Price_, Jan 17 2015

%E a(25)-a(27) derived from A098959 by _Robert Price_, Jul 13 2023