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

121, 1118111, 1111161111, 11111164111111, 111111111512111111111, 1111111111114096111111111111, 111111111111181921111111111111, 111111111111111638411111111111111, 111111111111111111262144111111111111111111, 11111111111111111111104857611111111111111111111

Offset: 1

Author

Altug Alkan, Oct 02 2015

Keywords

• nonn
• base

Comments

Inspiration was symmetry and visual simplicity.

Examples

			a(1) = 121 because the concatenation of 1, 2 and 1 is a semiprime number.
a(2) = 1118111 because the concatenation of 111, 8 and 111 is a semiprime number.
a(3) = 1111161111 because the concatenation of 1111, 16 and 1111 is a semiprime number.
		

Crossrefs

Cf. A001358, A002275, A068817, A070220, A070746, A262399.

Programs

Maple

ncat:= (a,b) -> 10^(1+ilog10(b))*a+b:
f:= proc(n) local N;
  N:= ncat(ncat((10^n-1)/9,2^n),(10^n-1)/9);
  if numtheory:-bigomega(N) = 2 then N else NULL fi
end proc:
seq(f(n),n=1..25); # Robert Israel, Oct 04 2015

Mathematica

Select[Table[FromDigits[Flatten[{PadRight[{},n,1],IntegerDigits[2^n],PadRight[{},n,1]}]],{n,20}], PrimeOmega[#]==2&] (* Harvey P. Dale, Dec 02 2023 *)

PARI

for(n=1, 25, if(bigomega(k=eval(Str((10^n - 1)/9, 2^n, (10^n - 1)/9))) == 2, print1(k", ")))