A275020 - OEIS

%I #22 May 25 2024 17:37:41

%S 1,2,3,10,19,35,43,80,107,143,199,218,255,304,353,560,904,996,1051,

%T 6141,8075,9913,11151,28469,75244,108960,122592,178206,187471,257431

%N Numbers k such that (5*10^k + 91) / 3 is prime.

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

%C a(31) > 3*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 16w97</a>.

%e 3 is in this sequence because (5*10^3 + 91) / 3 = 1697 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 47;

%e a(2) = 2, 197;

%e a(3) = 3, 1697;

%e a(4) = 10, 16666666697;

%e a(5) = 19, 16666666666666666697, etc.

%t Select[Range[0, 100000], PrimeQ[(5*10^# + 91) / 3] &]

%o (PARI) is(n)=ispseudoprime((5*10^n + 91)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,2

%A _Robert Price_, Nov 12 2016

%E a(26)-a(29) from _Robert Price_, Apr 28 2018

%E a(30) from _Robert Price_, Oct 25 2023