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Values of k such that 3^k is a concatenation of two primes.
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%I #10 Apr 17 2024 16:45:38

%S 3,5,6,9,10,15,17,19,28,35,42,47,51,55,56,58,63,73,80,83,85,87,94,100,

%T 112,127,129,132,198,202,268,282,287,299,316,325,345,362,400,412,447,

%U 459,519,525,549,620,631,727,756,854,856,892,1031,1038,1140,1175,1241

%N Values of k such that 3^k is a concatenation of two primes.

%e 3^3 = 27 = concat(2,7);

%e 3^5 = 243 = concat(2,43);

%e 3^6 = 729 = concat(7,29);

%e 3^9 = 19683 = concat(19,683).

%p with(numtheory): P:= proc(q) local a,k,n,ok; a:=0;

%p for n from 1 to q do ok:=0;

%p for k from 1 to ilog10(3^n) do if isprime(trunc(3^n/10^k)) and isprime(3^n mod 10^k) then ok:=1;

%p break; fi; od; if ok=1 then a:=a+1; lprint(a,n); fi; od; end: P(10^10);

%t ctpQ[k_]:=AnyTrue[Boole[PrimeQ[Table[FromDigits/@TakeDrop[IntegerDigits[3^k],n],{n,IntegerLength[ 3^k-1]}]]],#=={1,1}&]; Select[Range[1250],ctpQ] (* _Harvey P. Dale_, Apr 17 2024 *)

%Y Cf. A255898.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Oct 23 2015