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Numbers k such that 5*10^k + 77 is prime.
0

%I #16 May 02 2024 04:26:44

%S 1,2,3,4,6,8,19,27,37,56,66,136,148,387,534,536,1273,1593,1796,2026,

%T 2164,2502,6128,18714,23327,25427,46461,88182,88377,104326,127153,

%U 135019

%N Numbers k such that 5*10^k + 77 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 77 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 50w77</a>.

%e 3 is in this sequence because 5*10^3 + 77 = 5077 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 127;

%e a(2) = 2, 577;

%e a(3) = 3, 5077;

%e a(4) = 4, 50077;

%e a(5) = 6, 5000077, etc.

%t Select[Range[0, 100000], PrimeQ[5*10^# + 77] &]

%o (PARI) is(n)=ispseudoprime(5*10^n + 77) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,2

%A _Robert Price_, Jun 23 2016

%E a(30)-a(32) from _Robert Price_, Dec 30 2018