A255325 Half of the difference between the n-th Ludic number and the n-th noncomposite: a(n) = (A003309(n) - A008578(n))/2.

0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 3, 2, 1, 2, 3, 4, 4, 5, 5, 6, 8, 6, 7, 9, 9, 9, 9, 10, 11, 15, 11, 13, 12, 17, 13, 14, 12, 15, 21, 19, 21, 21, 18, 20, 19, 20, 18, 17, 19, 24, 25, 24, 30, 28, 28, 33, 31, 33, 32, 36, 38, 34, 35, 36, 38, 40, 38, 39, 36, 36, 39, 37, 35, 36, 42, 42, 43, 42, 46, 44, 42, 44, 43, 47, 48, 49, 52

Offset: 1

Author

Antti Karttunen, Feb 23 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003309, A008578.

Cf. A255324 (the same terms multipled by 2).

Programs

Mathematica

t = Range[2, 1000];
A003309 = {1};
While[Length[t] > 0, k = First[t];
     AppendTo[A003309, k]; t = Drop[t, {1, -1, k}]];
a[n_] := If[n == 1, 0, A003309[[n]] - Prime[n - 1]]/2;
Array[a, Length[A003309]] (* Jean-François Alcover, Jan 08 2022, after Ray Chandler in A003309 *)

Scheme

(define (A255325 n) (/ (A255324 n) 2))

Formula

a(n) = A255324(n)/2 = (A003309(n) - A008578(n))/2.