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A295967 Numbers k such that (35*10^k - 377)/9 is prime. 0

%I #12 Jan 17 2019 13:44:10

%S 2,3,6,24,33,86,335,711,1103,1169,1181,2163,3026,7940,8174,9365,10127,

%T 13466,40130,70130,174704,198294

%N Numbers k such that (35*10^k - 377)/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 47 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 38w47</a>

%e 2 is in this sequence because (35*10^2 - 377)/9 = 347 is prime.

%e Initial terms and primes associated:

%e a(1) = 2, 347;

%e a(2) = 3, 3847;

%e a(3) = 6, 3888847;

%e a(4) = 24, 3888888888888888888888847;

%e a(5) = 33, 3888888888888888888888888888888847; etc.

%t Select[Range[2, 100000], PrimeQ[(35*10^# - 377)/9] &]

%o (PARI) isok(k) = isprime((35*10^k - 377)/9); \\ _Michel Marcus_, Dec 01 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 30 2017

%E a(21)-a(22) from _Robert Price_, Jul 19 2018

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Last modified April 19 17:51 EDT 2024. Contains 371797 sequences. (Running on oeis4.)