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Numbers k such that 2*10^k + 51 is prime.
0

%I #13 May 27 2024 02:08:39

%S 0,1,2,4,8,22,68,70,109,112,144,154,318,418,451,536,638,1540,1590,

%T 2935,3859,8770,9860,70688,133955,161766,166458

%N Numbers k such that 2*10^k + 51 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 0 followed by the digits 51 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 20w51</a>.

%e 2 is in this sequence because 2*10^2 + 51 = 251 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 53;

%e a(2) = 1, 71;

%e a(3) = 2, 251;

%e a(4) = 4, 20051;

%e a(5) = 8, 200000051; etc.

%t Select[Range[0, 100000], PrimeQ[2*10^# + 51] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 19 2017

%E a(25)-a(27) from _Robert Price_, May 30 2018