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A290431 Numbers k such that (73*10^k + 413)/9 is prime. 0

%I #15 Jun 18 2019 09:59:44

%S 1,2,4,5,7,16,31,34,44,68,145,158,227,499,643,970,1004,1951,2923,3092,

%T 28069,48334,76262

%N Numbers k such that (73*10^k + 413)/9 is prime.

%C For k > 1, numbers such that the digit 8 followed by k-2 occurrences of the digit 1 followed by the digits 57 is prime (see Example section).

%C a(24) > 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 81w57</a>.

%e 4 is in this sequence because (73*10^4 + 413)/9 = 81157 is prime.

%e Initial terms and primes associated:

%e a(1) = 1, 127;

%e a(2) = 2, 857;

%e a(3) = 4, 81157;

%e a(4) = 5, 811157;

%e a(5) = 7, 81111157; etc.

%t Select[Range[0, 100000], PrimeQ[(73*10^# + 413)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 06 2017

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)