|
%I #48 Dec 02 2023 13:39:45
%S 121,1118111,1111161111,11111164111111,111111111512111111111,
%T 1111111111114096111111111111,111111111111181921111111111111,
%U 111111111111111638411111111111111,111111111111111111262144111111111111111111,11111111111111111111104857611111111111111111111
%N Semiprimes that are the concatenation of n 1's, 2^n and n 1's
%C Inspiration was symmetry and visual simplicity.
%e a(1) = 121 because the concatenation of 1, 2 and 1 is a semiprime number.
%e a(2) = 1118111 because the concatenation of 111, 8 and 111 is a semiprime number.
%e a(3) = 1111161111 because the concatenation of 1111, 16 and 1111 is a semiprime number.
%p ncat:= (a,b) -> 10^(1+ilog10(b))*a+b:
%p f:= proc(n) local N;
%p N:= ncat(ncat((10^n-1)/9,2^n),(10^n-1)/9);
%p if numtheory:-bigomega(N) = 2 then N else NULL fi
%p end proc:
%p seq(f(n),n=1..25); # _Robert Israel_, Oct 04 2015
%t Select[Table[FromDigits[Flatten[{PadRight[{},n,1],IntegerDigits[2^n],PadRight[{},n,1]}]],{n,20}], PrimeOmega[#]==2&] (* _Harvey P. Dale_, Dec 02 2023 *)
%o (PARI) for(n=1, 25, if(bigomega(k=eval(Str((10^n - 1)/9, 2^n, (10^n - 1)/9))) == 2, print1(k", ")))
%Y Cf. A001358, A002275, A068817, A070220, A070746, A262399.
%K nonn,base
%O 1,1
%A _Altug Alkan_, Oct 02 2015
|
