Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 May 18 2024 11:31:46
%S 1,2,5,7,8,11,17,61,73,89,197,233,308,2096,3170,8003,15014,16166,
%T 26021,55748,102533,171601
%N Numbers k such that (536*10^k - 23)/9 is prime.
%C For k>1, numbers k such that the digits 59 followed by k-1 occurrences of the digit 5 followed by the digit 3 is prime (see Example section).
%C a(23) > 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 595w3</a>.
%e 2 is in this sequence because (536*10^2 - 23)/9 = 5953 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 593;
%e a(2) = 2, 5953;
%e a(3) = 5, 5955553;
%e a(4) = 7, 595555553;
%e a(5) = 8, 5955555553; etc.
%t Select[Range[0, 100000], PrimeQ[(536*10^# - 23)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 05 2017
%E a(21)-a(22) from _Robert Price_, Feb 23 2020