|
%I #13 Jan 21 2019 20:14:10
%S 0,1,2,3,8,18,20,24,40,57,84,92,111,135,138,272,423,540,542,1147,1246,
%T 1713,2217,2767,3486,30586,34183,61119,113658,194668
%N Numbers k such that 4*10^k + 49 is prime.
%C For k > 1, numbers such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 49 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/primedifficulty.txt">Search for 40w49.</a>
%e 3 is in this sequence because 4*10^3 + 49 = 4049 is prime.
%e Initial terms and primes associated:
%e a(1) = 0, 53;
%e a(2) = 1, 89;
%e a(3) = 2, 449;
%e a(4) = 3; 4049;
%e a(5) = 8, 400000049; etc.
%t Select[Range[0, 100000], PrimeQ[4*10^# + 49] &]
%o (PARI) isok(k) = ispseudoprime(4*10^k + 49) \\ _Altug Alkan_, Aug 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Aug 13 2017
%E a(29)-a(30) from _Robert Price_, Jan 21 2019
|
