|
%I #23 Jul 12 2023 12:58:38
%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/primedifficulty.txt">Search for 303w7</a>.
%e 4 is in this sequence because (91*10^4+11)/3 = 303337 is prime.
%e Initial terms and primes associated:
%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
|
