A282571 - OEIS

%I #14 Jun 08 2024 05:44:02

%S 2,3,4,9,26,40,41,56,82,114,150,155,203,213,578,2638,4761,10202,14211,

%T 16421,18047,30701,53834,66826,115784,141407

%N Numbers k such that 2*10^k - 27 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 73 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/prime_difficulty.txt">Search for 19w73</a>.

%e 3 is in this sequence because 2*10^3 - 27 = 1973 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 173;

%e a(2) = 3, 1973;

%e a(3) = 4, 19973;

%e a(4) = 9, 1999999973;

%e a(5) = 26, 199999999999999999999999973; etc.

%t Select[Range[2, 100000], PrimeQ[2*10^# - 27] &]

%o (PARI) isok(k) = isprime(2*10^k - 27); \\ _Michel Marcus_, Feb 19 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 18 2017

%E a(25)-a(26) from _Robert Price_, May 05 2018