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A281643 Numbers k such that 7*10^k - 69 is prime. 0

%I #14 Jul 10 2023 10:06:23

%S 2,4,5,12,29,34,53,56,161,287,312,436,468,672,1316,1642,2814,4171,

%T 6409,6657,7914,9259,9997,21253,29180,37246,47936,48816,49580,92414,

%U 97874,105131,119006,137153,151309,155450

%N Numbers k such that 7*10^k - 69 is prime.

%C For k>1, numbers such that the digit 6 followed by k-2 occurrences of the digit 9 followed by the digits 31 is prime (see Example section).

%C a(37) > 3*10^5. - _Robert Price_, Jul 10 2023

%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 69w31</a>.

%e 4 is in this sequence because 7*10^4 - 69 = 69931 is prime.

%e Initial terms and primes associated:

%e a(1) = 2, 631;

%e a(2) = 4, 69931;

%e a(3) = 5, 699931;

%e a(4) = 12, 6999999999931;

%e a(5) = 29, 699999999999999999999999999931; etc.

%t Select[Range[1, 100000], PrimeQ[7*10^# - 69] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jan 25 2017

%E a(32)-a(36) from _Robert Price_, Jul 03 2019

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)