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Numbers k such that 10^k - 701 is prime.
0

%I #14 May 25 2024 14:27:59

%S 7,13,22,28,29,49,53,70,124,151,287,394,400,946,979,1270,3857,3944,

%T 5435,9125,9589,49711,51091,56849

%N Numbers k such that 10^k - 701 is prime.

%C For k > 2, numbers k such that k-3 occurrences of the digit 9 followed by the digits 299 is prime (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 9w299</a>.

%e 7 is in this sequence because 10^7 - 701 = 9999299 is prime.

%e Initial terms and associated primes:

%e a(1) = 7, 9999299;

%e a(2) = 13, 9999999999299;

%e a(3) = 22, 9999999999999999999299;

%e a(4) = 28, 9999999999999999999999999299;

%e a(5) = 29, 99999999999999999999999999299; etc.

%t Select[Range[3, 100000], PrimeQ[10^# - 701] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jun 12 2017