A131866 Distance of n-th semiprime to nearest square.

0, 2, 0, 1, 2, 1, 4, 3, 0, 1, 3, 2, 1, 2, 3, 3, 0, 2, 6, 7, 6, 2, 1, 5, 7, 4, 1, 4, 5, 6, 9, 7, 6, 5, 6, 10, 6, 3, 2, 0, 1, 2, 8, 11, 10, 3, 2, 1, 1, 2, 11, 11, 10, 8, 3, 0, 8, 9, 13, 11, 9, 2, 5, 6, 7, 9, 10, 13, 12, 11, 10, 8, 7, 6, 4, 1, 10, 12, 9, 7, 3, 2, 3, 6, 9, 11, 15, 11, 2, 0, 2, 6, 9, 10, 12

Offset: 1

Author

Jonathan Vos Post, Oct 04 2007

Keywords

• easy
• nonn

Comments

This to semiprimes A001358 as A047972 is to primes A000040.

For each semiprime, find the closest square (preceding or succeeding); subtract, take absolute value.

Examples

			a(1) = 0 because the first semiprime is 4, which is a square.
a(2) = 2 because the 2nd semiprime is 6 and |6-4| = 2 where 4 is the nearest square to 6.
a(3) = 0 because the 3rd semiprime is 9, which is a square.
a(4) = 1 because the 4th semiprime is 10 and |10-9| = 1 where 9 is the nearest square to 10.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A047972, A053188.

Programs

Mathematica

dns[n_]:=Min[n-Floor[Sqrt[n]]^2,Ceiling[Sqrt[n]]^2-n]; dns/@Select[ Range[ 400],PrimeOmega[#]==2&] (* Harvey P. Dale, Aug 12 2016 *)

Formula

a(n)=A053188(A001358(n)) (corrected by R. J. Mathar, Nov 19 2007).

Extensions

More terms from R. J. Mathar, Oct 24 2007