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A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0. 3

%I

%S 0,2,4,5,6,11,15,16,21,23,34,114,119,357,1487,1818,4678,9820,27216,

%T 27692,194412

%N Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.

%C Numbers n such that 20*10^n + 3 is prime.

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

%C Numbers corresponding to terms <= 357 are certified primes.

%C a(21) > 10^5. - _Robert Price_, Nov 16 2014

%C a(22) > 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/2/20003.htm#prime">Prime numbers of the form 200...003</a>.

%F a(n) = A081677(n+1) - 1. - _Robert Price_, Nov 16 2014

%e 2003 is prime, hence 2 is a term.

%t Select[Range[0, 1000], PrimeQ[(20 10^# + 3)] &] (* _Vincenzo Librandi_, Nov 17 2014 *)

%o (PARI) a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

%o (PARI) for(n=0,1500,if(isprime(20*10^n+3),print1(n,",")))

%o (MAGMA) [n: n in [0..500] | IsPrime(20*10^n+3)]; // _Vincenzo Librandi_, Nov 17 2014

%Y Cf. A000533, A002275, A081677.

%K nonn,hard,more

%O 1,2

%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(19)-a(20) derived from A081677 by _Robert Price_, Nov 16 2014

%E a(21) from _Robert Price_, Jul 11 2015

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)