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Numbers k such that (26*10^k - 89) / 9 is prime.
0

%I #19 May 26 2024 14:59:02

%S 1,3,4,13,15,21,27,63,70,123,136,178,208,265,411,457,856,2401,4642,

%T 8017,8211,8385,12337,20793,123970,189928

%N Numbers k such that (26*10^k - 89) / 9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 8 followed by the digits 79 is prime (see Example section).

%C a(27) > 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 28w79</a>.

%e 4 is in this sequence because (26*10^4 - 89) / 9 = 28879 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 19;

%e a(2) = 3, 2879;

%e a(3) = 4, 28879;

%e a(4) = 13, 28888888888879;

%e a(5) = 15, 2888888888888879; etc.

%t Select[Range[0, 100000], PrimeQ[(26*10^# - 89) / 9] &]

%o (PARI) is(n)=ispseudoprime((26*10^n-89)/9) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 21 2016

%E a(25)-a(26) from _Robert Price_, Jun 16 2018