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A358617 a(n) is the number of zeros among the first n terms of row n of the Gilbreath array shown in A036262. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 05:08 EST 2023. Contains 360112 sequences. (Running on oeis4.)