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A102008 Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 81 for n > 0. 1

%I #15 Jan 17 2019 13:44:07

%S 0,1,2,3,8,17,21,44,48,55,68,145,201,271,2729,2840,4561,31809,43185,

%T 48108,92690

%N Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 81 for n > 0.

%C Numbers n such that 10*10^n + 9 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 271 are certified primes.

%C a(22) > 2*10^5. - _Robert Price_, Oct 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/1/10009.htm#prime">Prime numbers of the form 100...009</a>.

%F a(n) = A088275(n) - 1.

%e 1009 is prime, hence 2 is a term.

%t Select[Range[0, 200000], PrimeQ[10*10^# + 9] &] (* _Robert Price_, Oct 11 2015 *)

%o (PARI) a=19;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-81)

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

%Y Cf. A000533, A002275, A088275.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

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

%E a(21) from Kamada data by _Ray Chandler_, May 01 2015

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)