login

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”).

Numbers k such that (16*10^k + 167)/3 is prime.
0

%I #11 Jun 02 2024 09:29:20

%S 0,1,5,8,12,13,14,15,33,98,123,260,485,1340,1674,1775,5988,7039,9421,

%T 15149,21751,30882,36517,85839,121633,131180,140091,188823

%N Numbers k such that (16*10^k + 167)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 89 is prime (see Example section).

%C a(29) > 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 53w89</a>.

%e 5 is in this sequence because (16*10^5 + 167)/3 = 533389 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 61;

%e a(2) = 1, 109;

%e a(3) = 5, 533389;

%e a(4) = 8, 533333389;

%e a(5) = 12, 5333333333389; etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# + 167)/3] &]

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 25 2017

%E a(25)-a(28) from _Robert Price_, Jun 18 2019