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

1,2

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.

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A001358, A047972, A053188.

Sequence in context: A020513 A029276 A109248 * A036862 A285124 A094238

Adjacent sequences: A131863 A131864 A131865 * A131867 A131868 A131869

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 04 2007

Extensions

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

Status

approved