A358617 a(n) is the number of zeros among the first n terms of row n of the Gilbreath array shown in A036262.

0, 0, 1, 2, 3, 3, 3, 3, 1, 8, 7, 5, 7, 9, 5, 8, 5, 9, 10, 10, 8, 9, 10, 11, 10, 10, 17, 12, 17, 12, 13, 8, 20, 22, 18, 17, 14, 25, 20, 24, 24, 22, 21, 15, 19, 25, 25, 25, 24, 24, 21, 23, 27, 24, 23, 29, 32, 19, 26, 36, 34, 34, 31, 27, 35, 38, 35, 37, 25, 37

Offset

1,4

Comments

Conjecture: If = (a(n)/n), then (lim inf S) > 2/5 and (lim sup S) < 3/5.

Links

Table of n, a(n) for n=1..70.

Example

Corner of Gilbreath array:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101
1 2 2 4  2  4  2  4  6  2  6  4  2  4  6  6  2  6  4  2  6  4  6  8  4   2
1 0 2 2  2  2  2  2  4  4  2  2  2  2  0  4  4  2  2  4  2  2  2  4  2   2
1 2 0 0  0  0  0  2  0  2  0  0  0  2  4  0  2  0  2  2  0  0  2  2  0   0
1 2 0 0  0  0  2  2  2  2  0  0  2  2  4  2  2  2  0  2  0  2  0  2  0   0
1 2 0 0  0  2  0  0  0  2  0  2  0  2  2  0  0  2  2  2  2  2  2  2  0   8
1 2 0 0  2  2  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  0  2  8   8
1 2 0 2  0  2  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  2  6  0   8
1 2 2 2  2  2  2  2  0  0  0  2  0  0  0  0  2  0  0  0  0  2  4  6  8   6
1 0 0 0  0  0  0  2  0  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  2   4

Mathematica

z = 2000; t = Prime[Range[z]]; r[1] = t; r[2] = Abs[Differences[t]];
r[n_] := r[n] = Abs[Differences[r[n - 1]]];
Table[Count[Take[r[n], n], 0], {n, 1, z/2}]

Crossrefs

Cf. A000040, A036262, A358616.

Sequence in context: A246577 A097032 A127661 * A008968 A162499 A350857

Adjacent sequences: A358614 A358615 A358616 * A358618 A358619 A358620

Keyword

nonn

Author

Clark Kimberling, Nov 23 2022

Status

approved