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A295397 Numbers k such that (35*10^k - 737)/9 is prime. 0

%I #11 Jan 17 2019 13:44:10

%S 2,7,13,20,26,73,103,268,383,527,1748,2848,4424,7933,8311,9700,14872,

%T 18218,31294,42032,55547,111232

%N Numbers k such that (35*10^k - 737)/9 is prime.

%C For k > 1, numbers such that the digit 3 followed by k-2 occurrences of the digit 8 followed by the digits 07 is prime (see Example section).

%C a(23) > 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 38w07</a>

%e 2 is in this sequence because (35*10^2 - 737)/9 = 307 is prime.

%e Initial terms and primes associated:

%e a(1) = 2, 307;

%e a(2) = 7, 38888807;

%e a(3) = 13, 38888888888807;

%e a(4) = 20, 388888888888888888807;

%e a(5) = 26, 388888888888888888888888807; etc.

%t Select[Range[2, 100000], PrimeQ[(35*10^# - 737)/9] &]

%o (PARI) isok(k) = isprime((35*10^k - 737)/9); \\ _Michel Marcus_, Nov 22 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 21 2017

%E a(22) from _Robert Price_, Jul 16 2018

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Last modified April 23 14:30 EDT 2024. Contains 371914 sequences. (Running on oeis4.)