A290115 - OEIS

%I #15 May 25 2024 13:54:07

%S 1,3,4,6,7,52,53,103,131,199,294,426,780,1144,1876,2001,3507,5737,

%T 6657,12558,28303,31608,60643,74741,124648

%N Numbers k such that (7*10^k + 197)/3 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see Example section).

%C a(26) > 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 23w99</a>.

%e 4 is in this sequence because (7*10^4 + 197)/3 = 23399 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 89;

%e a(2) = 3, 2399;

%e a(3) = 4, 23399;

%e a(4) = 6, 2333399;

%e a(5) = 7, 23333399; etc.

%p select(k -> isprime((7*10^k+197)/3), [$1..10000]); # _Robert Israel_, Jul 20 2017

%t Select[Range[0, 100000], PrimeQ[(7*10^# + 197)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jul 19 2017

%E a(25) from _Robert Price_, Jul 17 2018