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A294122 Numbers k such that 3*10^k + 37 is prime. 0

%I #13 Oct 26 2023 11:37:49

%S 1,2,3,7,9,15,18,23,39,147,1104,1158,1466,1514,1935,2149,2203,2553,

%T 2730,7169,9807,17684,23828,25824,27207,55679,94964,122977,206927

%N Numbers k such that 3*10^k + 37 is prime.

%C For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 37 is prime (see Example section).

%C a(30) > 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/primedifficulty.txt">Search for 30w37</a>

%e 2 is in this sequence because 3*10^2 + 37 = 337 is prime.

%e Initial terms and primes associated:

%e a(1) = 1, 67;

%e a(2) = 2, 337;

%e a(3) = 3, 3037;

%e a(4) = 7, 30000037;

%e a(5) = 9, 3000000037; etc.

%t Select[Range[0, 100000], PrimeQ[3*10^# + 37] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 23 2017

%E a(28) from _Robert Price_, Aug 15 2018

%E a(29) from _Robert Price_, Oct 26 2023

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)