A271822 - OEIS

%I #27 May 26 2024 16:02:18

%S 1,2,4,6,12,13,14,17,19,31,50,58,81,87,161,234,244,482,505,676,1111,

%T 1707,1929,2695,3819,7708,28958,44652,51508,56892,158862,160249,162410

%N Numbers k such that (91*10^k + 11)/3 is prime.

%C Numbers k such that the digits 30 followed by k-1 occurrences of the digit 3 followed by the digit 7 is prime (see Example section).

%C a(34) > 3*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 303w7</a>.

%e 4 is in this sequence because (91*10^4+11)/3 = 303337 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 307;

%e a(2) = 2, 3037;

%e a(3) = 4, 303337;

%e a(4) = 6, 30333337;

%e a(5) = 12, 30333333333337, etc.

%t Select[Range[0, 100000], PrimeQ[(91*10^# + 11)/3] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((91*10^n + 11)/3), print1(n, ", "))); \\ _Altug Alkan_, Apr 14 2016

%o (Magma) [n: n in [1..300] |IsPrime((91*10^n + 11) div 3)]; // _Vincenzo Librandi_, Apr 15 2016

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

%K nonn,more

%O 1,2

%A _Robert Price_, Apr 14 2016

%E a(31)-a(33) from _Robert Price_, Feb 15 2020