A358616 a(n) is the position of the first occurrence of the least term in row n of the Gilbreath array shown in A036262.

1, 1, 2, 3, 3, 3, 3, 3, 9, 2, 2, 2, 2, 2, 2, 3, 4, 2, 3, 5, 2, 2, 3, 3, 6, 2, 2, 2, 3, 4, 2, 6, 2, 2, 2, 3, 9, 2, 2, 2, 2, 2, 2, 3, 4, 2, 3, 4, 2, 5, 2, 2, 4, 2, 3, 3, 3, 9, 2, 2, 2, 2, 2, 2, 5, 2, 2, 3, 5, 2, 2, 3, 4, 2, 8, 2, 2, 2, 2, 2, 4, 2, 3, 3, 3, 3

Offset

1,3

Comments

Conjecture: Every positive integer occurs in this sequence.

Links

Table of n, a(n) for n=1..86.

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

t = Prime[Range[1000]]; r[1] = t; r[2] = Abs[Differences[t]];
r[n_] := r[n] = Abs[Differences[r[n - 1]]];
a[n_] := Select[Range[150], r[n][[#]] == 0  &, 1]
Join[{1, 1}, Flatten[Table[a[n], {n, 1, 120}]]]

Crossrefs

Cf. A000040, A036262, A358617.

Sequence in context: A103959 A035375 A354143 * A366105 A093493 A087162

Adjacent sequences: A358613 A358614 A358615 * A358617 A358618 A358619

Keyword

nonn

Author

Clark Kimberling, Nov 23 2022

Status

approved