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A101130 Indices of primes in sequence defined by A(0) = 79, A(k) = 10*A(k-1) - 81 for k > 0.

%I A101130 #35 Jul 11 2023 08:57:26
%S A101130 0,1,3,5,10,11,12,34,45,56,127,155,262,352,395,428,782,981,1057,1562,
%T A101130 1694,1815,1936,4235,4430,6857,9897,13144,16645,20890,63350,105295,
%U A101130 113692,121143,163779,234914,284750
%N A101130 Indices of primes in sequence defined by A(0) = 79, A(k) = 10*A(k-1) - 81 for k > 0.
%C A101130 Numbers k such that 70*10^k + 9 is prime.
%C A101130 Numbers k such that digit 7 followed by k >= 0 occurrences of digit 0 followed by digit 9 is prime.
%C A101130 Numbers corresponding to terms <= 981 are certified primes.
%C A101130 a(38) > 3*10^5. - _Robert Price_, Jul 10 2023
%D A101130 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A101130 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/70009.htm#prime">Prime numbers of the form 700...009</a>.
%H A101130 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F A101130 a(n) = A097954(n) - 1.
%e A101130 70009 is prime, hence 3 is a term.
%t A101130 Select[Range[0, 300], PrimeQ[70*10^# + 9] &] (* _Robert Price_, Sep 05 2015 *)
%o A101130 (PARI) a=79;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-81)
%o A101130 (PARI) for(n=0,1500,if(isprime(70*10^n+9),print1(n,",")))
%o A101130 (Magma) [n: n in [0..400] |IsPrime(70*10^n + 9)]; // _Vincenzo Librandi_, Sep 06 2015
%Y A101130 Cf. A000533, A002275, A097954.
%K A101130 nonn,hard,more
%O A101130 1,3
%A A101130 _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004
%E A101130 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E A101130 a(28)-a(31) from Kamada data by _Ray Chandler_, Apr 29 2015
%E A101130 a(32)-a(35) from _Robert Price_, Sep 05 2015
%E A101130 a(36)-a(37) from _Robert Price_, Jul 10 2023