A273265 - OEIS

%I #15 May 02 2024 04:24:36

%S 0,1,2,3,6,7,8,10,16,17,35,53,121,155,178,487,880,1153,2136,2790,2803,

%T 5775,5845,5971,7131,13213,13813,17153,31461,38735,93577,188457

%N Numbers k such that (16*10^k + 161)/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 87 is prime (see Example section).

%C a(33) > 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 53w87</a>.

%e 3 is in this sequence because (16*10^3 + 161)/3 = 5387 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 59;

%e a(2) = 1, 107;

%e a(3) = 2, 587;

%e a(4) = 3, 5387;

%e a(5) = 6, 5333387, etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# + 161)/3] &]

%o (PARI) is(n)=ispseudoprime((16*10^n + 161)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,3

%A _Robert Price_, May 18 2016

%E a(32) from _Robert Price_, Feb 27 2019