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%I #15 May 25 2024 15:05:44
%S 1,2,4,5,7,8,14,17,22,49,130,136,142,170,196,220,967,1816,2165,2542,
%T 2635,3979,10319,11096,12191,14381,14444,17558,18230,42176,113681
%N Numbers k such that (82*10^k + 161)/9 is prime.
%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 1 followed by the digits 29 is prime (see Example section).
%C a(32) > 2*10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 91w29</a>.
%e 4 is in this sequence because (82*10^4+161)/9 = 91129 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 109;
%e a(2) = 2, 929;
%e a(3) = 4, 91129;
%e a(4) = 5, 911129;
%e a(5) = 7, 91111129, etc.
%t Select[Range[0, 100000], PrimeQ[(82*10^# + 161)/9] &]
%o (PARI) is(n)=ispseudoprime((82*10^n + 161)/9) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Apr 08 2016
%E a(31) from _Robert Price_, Oct 31 2019
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