A276322 - OEIS

%I #21 Jun 02 2024 14:03:24

%S 1,2,5,7,17,18,25,60,64,66,118,125,1021,1901,2273,2524,6048,7098,8281,

%T 11634,13843,16098,18652,18661,20570,32291,34181,59928,65297,86546

%N Numbers k such that (13*10^k + 83) / 3 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 61 is prime (see Example section).

%C a(31) > 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 43w61</a>.

%e 5 is in this sequence because (13*10^5 + 83) / 3 = 433361 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 71;

%e a(2) = 2, 461;

%e a(3) = 5, 433361;

%e a(4) = 7, 43333361;

%e a(5) = 17, 433333333333333361, etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 83) / 3] &]

%o (PARI) is(n)=ispseudoprime((13*10^n + 83)/3) \\ _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_, Sep 01 2016