A131848 Least nonnegative number which when added to the n-th semiprime gives a multiple of n.

0, 0, 0, 2, 1, 3, 0, 2, 2, 4, 0, 2, 4, 4, 6, 2, 2, 3, 2, 3, 5, 4, 4, 3, 1, 1, 26, 27, 1, 3, 2, 3, 5, 7, 34, 33, 33, 34, 37, 39, 1, 3, 0, 43, 1, 43, 46, 1, 2, 4, 49, 50, 0, 1, 54, 55, 51, 54, 53, 55, 57, 54, 51, 54, 57, 59, 62, 63, 63, 66, 69, 71, 1, 3, 4, 2, 73, 75, 69, 71

Offset: 1

Author

Jonathan Vos Post, Oct 04 2007

Keywords

• easy
• nonn

Comments

This is to semiprimes A001358 as A068901 is to primes A000040.

Examples

			a(1) = 0 because 1 | (0+semiprime(1)=4).
a(6) = 3 because 6 | (3+semiprime(3)=3+15=18).
a(25) = 1 because 25 | (1+semiprime(25)=1+74=75).
		

Links

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

Crossrefs

Cf. A000040, A001358, A068901.

Programs

Mathematica

lnn[{s_,n_}]:=If[Divisible[s,n],0,n-Mod[s,n]]; lnn/@Module[{sp=Select[ Range[ 300], PrimeOmega[#] ==2&], len},len=Length[sp];Thread[{sp,Range[len]}]] (* Harvey P. Dale, Mar 23 2013 *)

Formula

a(n) = MIN{k=>0 such that n|(k+A001358(n))}.

Extensions

More terms from R. J. Mathar, Jan 15 2008