A294489 - OEIS

%I #19 May 18 2024 13:38:41

%S 0,1,4,6,12,28,39,58,73,102,141,409,423,567,831,930,1515,2619,5727,

%T 9235,12706,13189,37182,73917

%N Numbers k such that (77*10^k - 59)/9 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 5 followed by the digits 49 is prime (see Example section).

%C a(25) > 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/prime_difficulty.txt">Search for 85w49</a>.

%e 4 is in this sequence because (77*10^4 - 59)/9 = 85549 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 2;

%e a(2) = 1, 79;

%e a(3) = 4, 85549;

%e a(4) = 6, 8555549;

%e a(5) = 12, 8555555555549; etc.

%t Select[Range[0, 100000], PrimeQ[(77*10^# - 59)/9] &]

%o (PARI) isok(n) = isprime((77*10^n - 59)/9); \\ _Michel Marcus_, Nov 01 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 31 2017