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Numbers k such that 3*10^k + 77 is prime.
0

%I #29 Jun 15 2024 17:53:29

%S 1,6,9,10,11,16,17,21,108,180,324,340,606,700,1857,2447,2658,11055,

%T 16177,16439,18767,33173,47842,105582,107389,279271

%N Numbers k such that 3*10^k + 77 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 77 is prime (see Example section).

%C a(27) > 3*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 30w77</a>.

%e 6 is in this sequence because 3*10^6 + 77 = 3000077 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 107;

%e a(2) = 6, 3000077;

%e a(3) = 9, 3000000077;

%e a(4) = 10, 30000000077;

%e a(5) = 11, 300000000077; etc.

%t Select[Range[0, 100000], PrimeQ[3*10^# + 77] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 16 2017

%E a(24)-a(25) from _Robert Price_, Sep 01 2018

%E a(26) from _Robert Price_, Jun 15 2024