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A101849 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) + 27 for n > 0. 3

%I #20 Jan 17 2019 13:44:06

%S 0,1,13,19,29,43,65,259,871,8845,26743,57505,98471,106891

%N Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) + 27 for n > 0.

%C Numbers n such that (360*10^n - 27)/9 is prime.

%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 9 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 871 are certified primes.

%C a(14) > 10^5. - _Robert Price_, Mar 17 2015.

%C a(15) > 2*10^5. - _Robert Price_, Oct 02 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/3/39997.htm#prime">Prime numbers of the form 399...997</a>.

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

%F a(n) = A101398(n) - 1.

%e 397 is prime, hence 1 is a term.

%t Select[Range[0, 1000], PrimeQ[(360*10^# - 27)/9] &] (* _Robert Price_, Mar 17 2015 *)

%o (PARI) a=37;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+27)

%o (PARI) for(n=0,1500,if(isprime((360*10^n-27)/9),print1(n,",")))

%Y Cf. A000533, A002275, A101155, A169830, A101398.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

%E 8845 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(11)-a(13) derived from A101398 by _Robert Price_, Mar 17 2015

%E a(14) from _Robert Price_, Oct 02 2015

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)