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A261364
Semiprimes that are the concatenation of n 1's, 2^n and n 1's
2
121, 1118111, 1111161111, 11111164111111, 111111111512111111111, 1111111111114096111111111111, 111111111111181921111111111111, 111111111111111638411111111111111, 111111111111111111262144111111111111111111, 11111111111111111111104857611111111111111111111
OFFSET
1,1
COMMENTS
Inspiration was symmetry and visual simplicity.
EXAMPLE
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.
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 *)
PROG
(PARI) for(n=1, 25, if(bigomega(k=eval(Str((10^n - 1)/9, 2^n, (10^n - 1)/9))) == 2, print1(k", ")))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Altug Alkan, Oct 02 2015
STATUS
approved