|
%I #14 Sep 08 2022 08:46:17
%S 1,2,3,4,7,9,15,21,22,44,49,53,63,127,145,393,856,1006,1883,2263,5684,
%T 13324,14291,27435,38897,114076
%N Numbers k such that (4*10^k + 143) / 3 is prime.
%C For n>1, numbers such that the digit 1 followed by n-2 occurrences of the digit 3 followed by the digits 81 is prime (see Example section).
%C a(27) > 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/primedifficulty.txt">Search for 13w81.</a>
%e 2 is in this sequence because (4*10^2 + 143) / 3 = 1381 is prime.
%e Initial terms and primes associated:
%e a(1) = 1, 61;
%e a(2) = 2, 181;
%e a(3) = 3, 1381;
%e a(4) = 4, 13381;
%e a(5) = 7, 13333381, etc.
%t Select[Range[0, 100000], PrimeQ[(4*10^# + 143) / 3] &]
%o (PARI) is(n) = ispseudoprime((4*10^n + 143) / 3); \\ _Altug Alkan_, Sep 20 2016
%o (Magma) [n: n in [0..500] | IsPrime((4*10^n+143) div 3)]; // _Vincenzo Librandi_, Sep 22 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Sep 20 2016
%E a(26) from _Robert Price_, Mar 05 2018
|
