A272195 - OEIS

%I #14 May 25 2024 15:04:58

%S 1,2,4,5,7,8,13,16,22,112,134,139,250,445,475,512,544,1318,1588,3307,

%T 4216,4457,4474,4979,6241,9551,17939,20405,48106,54467,144797

%N Numbers k such that (64*10^k + 287)/9 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 1 followed by the digits 43 is prime (see Example section).

%C a(32) > 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 71w43</a>.

%e 5 is in this sequence because (64*10^5 + 287)/9 = 711143 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 103;

%e a(2) = 2, 743;

%e a(3) = 4, 71143;

%e a(4) = 5, 711143;

%e a(5) = 7, 71111143, etc.

%t Select[Range[0, 100000], PrimeQ[(64*10^#n + 287)/9] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((64*10^n + 287)/9), print1(n, ", "))); \\ _Altug Alkan_, Apr 22 2016

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

%K nonn,more

%O 1,2

%A _Robert Price_, Apr 22 2016

%E a(31) from _Robert Price_, Apr 13 2019