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Numbers k such that (151*10^k - 7)/9 is prime.
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%I #13 May 25 2024 14:27:55

%S 1,4,6,12,13,15,18,30,49,72,799,832,877,1122,1968,2046,8176,11976,

%T 16444,20896,32941,67027,94885,154434

%N Numbers k such that (151*10^k - 7)/9 is prime.

%C For k > 0, numbers k such that the digits 16 followed by k occurrences of the digit 7 (see Example section).

%C a(25) > 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 167w</a>.

%e 4 is in this sequence because (151*10^4 - 7)/9 = 167777 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 167;

%e a(2) = 4, 167777;

%e a(3) = 6, 16777777;

%e a(4) = 12, 16777777777777;

%e a(5) = 13, 167777777777777; etc.

%t Select[Range[0, 100000], PrimeQ[(151*10^# - 7)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jul 07 2017

%E a(24) from _Robert Price_, Jan 08 2020