A365938 Form the "Gilbreath Transform" array for the Euler phi function (A000010); sequence gives the third column, divided by 2.

1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1

Offset

1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

The first 4 rows of the Gilbreath Transform array for phi(n) are:
1, 1, 2, 2, 4, 2, 6, 4, 6, 4,10, 4,12, 6, 8, 8,16, 6,18, 8,12,10,22, 8,20
0, 1, 0, 2, 2, 4, 2, 2, 2, 6, 6, 8, 6, 2, 0, 8,10,12,10, 4, 2,12,14,12, 8
1, 1, 2, 0, 2, 2, 0, 0, 4, 0, 2, 2, 4, 2, 8, 2, 2, 2, 6, 2,10, 2, 2, 4, 2
0, 1, 2, 2, 0, 2, 0, 4, 4, 2, 0, 2, 2, 6, 6, 0, 0, 4, 4, 8, 8, 0, 2, 2, 2
The third column is 2, 0, 2, 2, ..., which when halved gives the current sequence 1, 0, 1, 1, ...
I conjecture that the first column is (1,0) repeated, and the second column is all 1's.

Mathematica

A365938list[nmax_]:=Module[{d=EulerPhi[Range[3, nmax+2]]}, Join[{1}, Table[First[d=Abs[Differences[d]]], nmax-1]/2]]; A365938list[200] (*  Paolo Xausa, Sep 25 2023 *)

Crossrefs

Cf. A000010, A036262, A361897.

Sequence in context: A127245 A175192 A088150 * A117567 A307183 A361433

Adjacent sequences: A365935 A365936 A365937 * A365939 A365940 A365941

Keyword

nonn

Author

N. J. A. Sloane, Sep 23 2023, following a suggestion from Sean A. Irvine

Status

approved