cp's OEIS Frontend

A261364 Semiprimes that are the concatenation of n 1's, 2^n and n 1's.

%I A261364 #50 Jul 23 2025 15:35:09
%S A261364 121,1118111,1111161111,11111164111111,111111111512111111111,
%T A261364 1111111111114096111111111111,111111111111181921111111111111,
%U A261364 111111111111111638411111111111111,111111111111111111262144111111111111111111,11111111111111111111104857611111111111111111111
%N A261364 Semiprimes that are the concatenation of n 1's, 2^n and n 1's.
%C A261364 Inspiration was symmetry and visual simplicity.
%e A261364 a(1) = 121 because the concatenation of 1, 2 and 1 is a semiprime number.
%e A261364 a(2) = 1118111 because the concatenation of 111, 8 and 111 is a semiprime number.
%e A261364 a(3) = 1111161111 because the concatenation of 1111, 16 and 1111 is a semiprime number.
%p A261364 ncat:= (a,b) -> 10^(1+ilog10(b))*a+b:
%p A261364 f:= proc(n) local N;
%p A261364   N:= ncat(ncat((10^n-1)/9,2^n),(10^n-1)/9);
%p A261364   if numtheory:-bigomega(N) = 2 then N else NULL fi
%p A261364 end proc:
%p A261364 seq(f(n),n=1..25); # _Robert Israel_, Oct 04 2015
%t A261364 Select[Table[FromDigits[Flatten[{PadRight[{},n,1],IntegerDigits[2^n],PadRight[{},n,1]}]],{n,20}], PrimeOmega[#]==2&] (* _Harvey P. Dale_, Dec 02 2023 *)
%o A261364 (PARI) for(n=1, 25, if(bigomega(k=eval(Str((10^n - 1)/9, 2^n, (10^n - 1)/9))) == 2, print1(k", ")))
%Y A261364 Cf. A001358, A002275, A068817, A070220, A070746, A262399.
%K A261364 nonn,base
%O A261364 1,1
%A A261364 _Altug Alkan_, Oct 02 2015