A295969 - OEIS

%I #15 May 03 2024 07:46:04

%S 2,3,4,9,10,16,27,46,97,103,214,229,241,285,643,999,3154,14115,43012,

%T 85855,87622,87712,90142,168379

%N Numbers k such that (5*10^k - 473)/9 is prime.

%C For k > 1, numbers k such that k-2 occurrences of the digit 5 followed by the digits 03 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 5w03</a>.

%e 3 is in this sequence because (5*10^3 - 473)/9 = 503 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 3;

%e a(2) = 3, 503;

%e a(3) = 4, 5503;

%e a(4) = 9, 555555503;

%e a(5) = 10, 5555555503; etc.

%t Select[Range[2, 100000], PrimeQ[(5*10^# - 473)/9] &]

%o (PARI) isok(k) = isprime((5*10^k - 473)/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(24) from _Robert Price_, Jan 21 2018