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A284886 Numbers k such that (14*10^k-101)/3 is prime. 0

%I #10 Feb 23 2019 11:03:49

%S 1,2,4,6,14,20,305,470,507,1104,1152,1725,1944,5864,6785,7446,11460,

%T 12412,16302,19787,24029,27240,67235,83471,89480,116112

%N Numbers k such that (14*10^k-101)/3 is prime.

%C For k>1, numbers such that the digit 4 followed by k-2 occurrences of the digit 6 followed by the digits 33 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/primedifficulty.txt">Search for 46w33.</a>

%e 4 is in this sequence because (14*10^4 - 101)/3 = 46633 is prime.

%e Initial terms and primes associated:

%e a(1) = 1, 13;

%e a(2) = 2, 433;

%e a(3) = 4, 46633;

%e a(4) = 6, 4666633;

%e a(5) = 14, 466666666666633; etc.

%t Select[Range[1, 100000], PrimeQ[(14*10^# - 101)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Apr 04 2017

%E a(26) from _Robert Price_, Feb 23 2019

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)