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Numbers k such that (26*10^k - 131)/3 is prime.
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%I #16 May 02 2024 04:23:51

%S 1,2,3,5,7,10,15,20,31,107,115,290,455,611,669,1190,2111,2147,2821,

%T 4094,4616,7087,7971,11416,12413,21475,23719,24435,32218,122625,

%U 160166,190789

%N Numbers k such that (26*10^k - 131)/3 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 23 is prime (see Example section).

%C a(33) > 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 86w23</a>.

%e 3 is in this sequence because (26*10^3 - 131)/3 = 8623 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 43;

%e a(2) = 2, 823;

%e a(3) = 3, 8623;

%e a(4) = 5, 866623;

%e a(5) = 7, 86666623, etc.

%t Select[Range[0, 100000], PrimeQ[(26*10^# - 131)/3] &]

%o (PARI) isok(n) = isprime((26*10^n - 131)/3); \\ _Michel Marcus_, Apr 28 2016

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

%K nonn,more

%O 1,2

%A _Robert Price_, Apr 28 2016

%E a(30)-a(32) from _Robert Price_, Oct 19 2019