A272999 - OEIS

%I #20 May 02 2024 04:24:27

%S 1,2,4,5,7,10,11,16,18,21,22,30,41,69,83,128,166,190,262,263,353,496,

%T 1398,1793,2806,9722,15733,32420,61095,77909,110496

%N Numbers k such that (11*10^k + 49)/3 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).

%C a(32) > 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 36w83</a>.

%e 4 is in this sequence because (11*10^4 + 49)/3 = 36683 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 53;

%e a(2) = 2, 383:

%e a(3) = 4, 36683;

%e a(4) = 5, 366683;

%e a(5) = 7, 36666683, etc.

%t Select[Range[0, 100000], PrimeQ[(11*10^# + 49)/3] &]

%o (PARI) is(n)=ispseudoprime((11*10^n + 49)/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_, May 12 2016

%E a(31) from _Robert Price_, Jul 19 2018