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A295395 Numbers k such that (61*10^k - 1)/3 is prime. 0

%I

%S 3,17,18,30,78,98,371,947,1085,1560,1607,2145,4310,4637,16674,17148,

%T 25209,27929,33491,74189

%N Numbers k such that (61*10^k - 1)/3 is prime.

%C Numbers such that the digits 20 followed by k occurrences of the digit 3 is prime (see Example section).

%C a(21) > 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 203w</a>

%e 3 is in this sequence because (61*10^3 - 1)/3 = 20333 is prime.

%e Initial terms and primes associated:

%e a(1) = 3, 20333;

%e a(2) = 17, 2033333333333333333;

%e a(3) = 18, 20333333333333333333;

%e a(4) = 30, 20333333333333333333333333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(61*10^# - 1)/3] &]

%o (PARI) isok(k) = isprime((61*10^k - 1)/3); \\ _Michel Marcus_, Nov 22 2017

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

%K nonn,more,hard,changed

%O 1,1

%A _Robert Price_, Nov 21 2017

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Last modified January 18 06:34 EST 2019. Contains 319269 sequences. (Running on oeis4.)