A293759 - OEIS

%I #19 May 27 2024 02:19:07

%S 1,2,4,7,8,19,26,28,38,43,67,331,359,832,907,1880,2359,4301,5896,6187,

%T 37154,40411,59584

%N Numbers k such that (35*10^k - 197)/9 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 8 followed by the digits 67 is prime (see Example section).

%C a(24) > 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 38w67</a>.

%e 2 is in this sequence because (35*10^2 - 197)/9 = 367 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 17;

%e a(2) = 2, 367;

%e a(3) = 4, 38867;

%e a(4) = 7, 38888867;

%e a(5) = 8, 388888867; etc.

%t Select[Range[1, 100000], PrimeQ[(35*10^# - 197)/9] &]

%o (Magma) [n: n in [1..400] |IsPrime((35*10^n - 197) div 9)]; // _Vincenzo Librandi_, Oct 16 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 15 2017

%E Comments, Link and Example corrected by _Robert Price_, Jun 11 2018