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%I #19 May 26 2024 16:02:05
%S 1,2,3,4,7,10,24,25,29,34,35,37,46,49,88,103,290,381,484,696,751,886,
%T 999,1750,5062,6214,9740,12558,16551,24674,28600,37427,48032,61991,
%U 70148,72516,99441,179656
%N Numbers k such that (68*10^k + 7)/3 is prime.
%C Numbers k such that the digits 22 followed by k-1 occurrences of the digit 6 followed by the digit 9 is prime (see Example section).
%C a(39) > 3*10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 226w9</a>.
%e 3 is in this sequence because (68*10^3+7)/3 = 22669 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 229;
%e a(2) = 2, 2269;
%e a(3) = 3, 22669;
%e a(4) = 4, 226669;
%e a(5) = 7, 226666669, etc.
%t Select[Range[0, 100000], PrimeQ[(68*10^# + 7)/3] &]
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((68*10^n + 7)/3), print1(n, ", "))); \\ _Altug Alkan_, Mar 20 2016
%Y Cf. A056654, A268448, A269303, A270339.
%K nonn,more
%O 1,2
%A _Robert Price_, Mar 20 2016
%E a(38) from _Robert Price_, Jan 16 2020