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 Jun 02 2024 14:04:49
%S 3,5,9,20,26,77,101,120,308,543,869,876,1193,1199,1355,1923,3689,3788,
%T 4182,6539,19068,26922,38957,58872,61230,72759
%N Numbers k such that (8*10^k + 67)/3 is prime.
%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 6 followed by the digits 89 is prime (see Example section).
%C a(27) > 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 26w89</a>.
%e 5 is in this sequence because (8*10^5 + 67)/3 = 2266689 7751 is prime.
%e Initial terms and associated primes:
%e a(1) = 3, 2689;
%e a(2) = 5, 266689;
%e a(3) = 9, 2666666689;
%e a(4) = 20, 266666666666666666689; etc.
%t Select[Range[0, 100000], PrimeQ[(8*10^# + 67)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Jan 28 2017