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Numbers k such that 8*10^k - 51 is prime.
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%I #23 Jun 08 2024 15:59:10

%S 1,3,5,28,90,209,220,226,301,352,516,1746,2214,2215,2364,2413,3043,

%T 3895,5837,8283,16551,20955,46161,67302,82360,94357,100439

%N Numbers k such that 8*10^k - 51 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 9 followed by the digits 49 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 79w49</a>.

%e 3 is in this sequence because 8*10^3 - 51 = 7949 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 29;

%e a(2) = 3, 7949;

%e a(3) = 5, 799949;

%e a(4) = 28, 79999999999999999999999999949; etc.

%t Select[Range[1, 100000], PrimeQ[8*10^# - 51] &]

%o (PARI) is(n) = ispseudoprime(8*10^n-51) \\ _Felix Fröhlich_, Aug 12 2019

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 06 2017

%E a(27) from _Robert Price_, Aug 12 2019