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A293281 Numbers k such that (28*10^k + 149)/3 is prime. 0

%I #13 Dec 08 2019 12:27:14

%S 0,2,4,6,10,20,40,42,46,60,68,128,516,816,1062,3204,3682,4964,5722,

%T 11442,17856,41058,60180,85500,104972

%N Numbers k such that (28*10^k + 149)/3 is prime.

%C For k > 1, numbers such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 83 is prime (see Example section).

%C a(26) > 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 93w83</a>.

%e 4 is in this sequence because (28*10^4 + 149)/3 = 93383 is prime.

%e Initial terms and primes associated:

%e a(1) = 0, 59;

%e a(2) = 2, 983;

%e a(3) = 4, 93383;

%e a(4) = 6, 9333383;

%e a(5) = 10, 93333333383; etc.

%t Select[Range[0, 100000], PrimeQ[(28*10^# + 149)/3] &]

%t Join[{0},Flatten[Position[Table[100*FromDigits[PadRight[{9},n,3]]+83,{n,86000}],_?PrimeQ]]+1] (* _Harvey P. Dale_, Nov 01 2017 *)

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 04 2017

%E a(25) from _Robert Price_, Dec 08 2019

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