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Numbers k such that 5*10^k - 13 is prime.
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%I #15 May 27 2024 02:04:50

%S 1,2,3,15,20,30,90,120,125,141,326,464,491,494,540,558,822,1103,1463,

%T 1638,1898,3332,10671,24842,37412,48855,173904

%N Numbers k such that 5*10^k - 13 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 9 followed by the digits 87 is prime (see Example section).

%C a(28) > 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 49w87</a>.

%e 2 is in this sequence because 5*10^2 - 13 = 487 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 37;

%e a(2) = 2, 487;

%e a(3) = 3, 4987;

%e a(4) = 15, 4999999999999987;

%e a(5) = 20, 499999999999999999987; etc.

%p select(k->isprime(5*10^k-13),[$1..1000]); # _Muniru A Asiru_, Jan 03 2019

%t Select[Range[1, 100000], PrimeQ[5*10^# - 13] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 23 2017

%E a(27) from _Robert Price_, Jan 03 2019