A358468 Number of 2's that appeared by n-th step when constructing A030717.

0, 0, 1, 2, 3, 3, 3, 3, 4, 6, 8, 9, 10, 11, 12, 14, 16, 19, 23, 26, 27, 29, 32, 38, 43, 48, 51, 56, 63, 71, 79, 87, 94, 101, 109, 116, 125, 133, 140, 149, 161, 174, 188, 202, 217, 233, 250, 266, 284, 304, 326, 347, 369, 392, 418, 444, 471, 499, 530, 561, 593, 625, 658, 692, 726, 761, 797, 833, 869, 906, 944

Offset: 1

Author

Seiichi Manyama, Nov 18 2022

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1024
• Michael De Vlieger, Plot of the n-th row of A030717 n = 1..512, showing 2's in red and all other terms in blue.

Crossrefs

Partial sums of A358469.

Cf. A030717, A358466.

Programs

Mathematica

nn = 94; c[] = 0; k = a[1] = c[1] = 1; Accumulate@ Prepend[Reap[Do[w = Union@ Array[a, k]; t = 0; Do[Set[a[j + k], c[w[[j]]]]; If[a[j + k] == 2, t++], {j, Length[w]}]; Do[c[a[j + k]]++, {j, Length[w]}]; k += Length[w]; Sow[t], {n, nn}]][[-1, -1]], 0] (* _Michael De Vlieger, Nov 18 2022 *)

Ruby

def A(k, n)
  a = []
  ary = [1]
  n.times{
    a << ary.count(k)
    ary += ary.uniq.sort.map{|i| ary.count(i)}
  }
  a
end
p A(2, 100)