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Numbers k such that (49*10^k - 67)/9 is prime.
1

%I #12 Jun 02 2024 20:58:59

%S 1,3,4,7,10,24,37,46,63,64,91,114,367,453,1156,1347,1524,7153,10893,

%T 13548,15153,43093,61167,184993

%N Numbers k such that (49*10^k - 67)/9 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 37 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 54w37</a>.

%e 4 is in this sequence because (49*10^4 - 67)/9 = 54437 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 47;

%e a(2) = 3, 5437;

%e a(3) = 4, 54437;

%e a(4) = 7, 54444437;

%e a(5) = 10, 54444444437; etc.

%t Select[Range[1, 100000], PrimeQ[(49*10^# - 67)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 27 2017

%E a(24) from _Robert Price_, Mar 15 2019