A192512 Number of ludic numbers (A003309) not greater than n.

1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 19

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2011

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003309.

Cf. A192490 (first differences), A000720 (number of primes).

Programs

Haskell

a192512 n = a192512_list !! (n-1)
a192512_list = scanl1 (+) $ map a192490 [1..]

Mathematica

a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
ludicQ[n_, nmax_] /; 1 <= n <= nmax := MemberQ[a3309[nmax], n];
nmax = 100;
b[n_] := Boole[ludicQ[n, nmax]];
Array[b, nmax] // Accumulate (* Jean-François Alcover, Dec 09 2021, after Ray Chandler in A003309 *)

Formula

a(n) = #{A003309(k): 1<=k<=n} = Sum_{k=1..n} A192490(k).