|
%I #28 May 02 2024 04:26:55
%S 1,2,3,4,6,22,25,29,59,89,221,453,535,1708,2242,2413,3581,4234,4848,
%T 5380,6548,8654,11035,17308,27634,28807,35481,79678,80875,114658,
%U 230394
%N Numbers k such that (26*10^k - 119)/3 is prime.
%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 27 is prime (see Example section).
%C a(32) > 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 86w27</a>.
%e 3 is in this sequence because (26*10^3 - 119)/3 = 8627 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 47;
%e a(2) = 2, 827;
%e a(3) = 3, 8627;
%e a(4) = 4, 86627;
%e a(5) = 6, 8666627, etc.
%t Select[Range[0, 100000], PrimeQ[(26*10^# - 119)/3] &]
%o (Magma) [n: n in [1..500] |IsPrime((26*10^n-119) div 3)]; // _Vincenzo Librandi_, Jul 07 2016
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((26*10^n-119)/3), print1(n, ", "))); \\ _Altug Alkan_, Jul 08 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Jul 06 2016
%E a(30)-a(31) from _Robert Price_, Jul 12 2023
|
