A295667 - OEIS

%I #13 May 03 2024 07:45:19

%S 1,10,16,19,28,43,76,91,125,203,283,911,2416,2633,4735,4876,4900,7825,

%T 26969,51154,169019

%N Numbers k such that (22*10^k + 383)/9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 4 followed by the digits 87 is prime (see Example section).

%C a(22) > 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 24w87</a>.

%e 1 is in this sequence because (22*10^1 + 383)/9 = 67 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 67;

%e a(2) = 10, 24444444487;

%e a(3) = 16, 24444444444444487;

%e a(4) = 19, 24444444444444444487;

%e a(5) = 28, 24444444444444444444444444487; etc.

%t Select[Range[0, 100000], PrimeQ[(22*10^# + 383)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 25 2017

%E a(21) from _Robert Price_, May 27 2018