A280632 - OEIS

%I #15 Jun 02 2024 14:04:24

%S 1,3,4,9,10,11,14,25,38,74,110,133,145,469,1035,1808,3323,4534,4875,

%T 5306,16645,20591,25904,29365,81488,108184,132550

%N Numbers k such that (19*10^k + 191)/3 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

%C a(28) > 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 63w97</a>.

%e 4 is in this sequence because (19*10^4 + 191) / 3 = 63397 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 127;

%e a(2) = 3, 6397;

%e a(3) = 4, 63397;

%e a(4) = 9, 6333333397;

%e a(5) = 10, 63333333397; etc.

%t Select[Range[0, 100000], PrimeQ[(19*10^# + 191) / 3] &]

%o (PARI) isok(n) = isprime((19*10^n + 191)/3); \\ _Michel Marcus_, Jan 07 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 06 2017

%E a(26)-a(27) from _Robert Price_, May 09 2019