A275285 - OEIS

%I #14 May 02 2024 04:26:08

%S 1,2,5,6,30,58,66,127,138,179,287,520,767,954,966,1254,1313,1976,2266,

%T 2496,3137,4058,4411,7009,11736,12155,21328,31124,31589,38581,42683,

%U 54634,56634,85297

%N Numbers k such that 33*10^k + 7 is prime.

%C For k > 0, numbers k such that the digits 33 followed by k-1 occurrences of the digit 0 followed by the digit 7 is prime (see Example section).

%C a(35) > 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 330w7</a>.

%e 5 is in this sequence because 33*10^5 + 7 = 3300007 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 337;

%e a(2) = 2, 3307;

%e a(3) = 5, 3300007;

%e a(4) = 6, 33000007;

%e a(5) = 30, 33000000000000000000000000000007, etc.

%t Select[Range[0, 100000], PrimeQ[33*10^# + 7] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(33*10^n+7), print1(n, ", "))); \\ _Altug Alkan_, Jul 21 2016

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

%K nonn,more

%O 1,2

%A _Robert Price_, Jul 21 2016