%I #12 Jan 17 2019 13:44:10
%S 3,19,27,145,166,196,247,345,370,799,1093,2877,5223,9157,22927,24600,
%T 25546,29424,82540,95451,159438
%N Numbers k such that (17*10^k - 377)/9 is prime.
%C For k > 1, numbers such that the digit 1 followed by k-2 occurrences of the digit 8 followed by the digits 47 is prime (see Example section).
%C a(22) > 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 18w47</a>
%e 3 is in this sequence because (17*10^3 - 377)/9 = 1847 is prime.
%e Initial terms and primes associated:
%e a(1) = 3, 1847;
%e a(2) = 19, 18888888888888888847;
%e a(3) = 27, 1888888888888888888888888847; etc.
%t Select[Range[2, 100000], PrimeQ[(17*10^# - 377)/9] &]
%o (PARI) isok(k) = isprime((17*10^k - 377)/9); \\ _Michel Marcus_, Nov 20 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Nov 19 2017
%E a(21) from _Robert Price_, Mar 24 2018
|