A334595 Binary interpretation of the right diagonal of the XOR-triangle with first row generated from the binary expansion of n.

1, 1, 2, 1, 6, 3, 4, 1, 14, 4, 11, 2, 13, 7, 8, 1, 30, 11, 20, 7, 24, 13, 18, 3, 28, 9, 22, 5, 26, 15, 16, 1, 62, 20, 43, 13, 50, 24, 39, 5, 58, 16, 47, 9, 54, 28, 35, 2, 61, 23, 40, 14, 49, 27, 36, 6, 57, 19, 44, 10, 53, 31, 32, 1, 126, 43, 84, 24, 103, 50

Offset

1,3

Comments

An XOR-triangle is an inverted 0-1 triangle formed by choosing a top row and having each entry in the subsequent rows be the XOR of the two values above it.

a(n) = n if and only if n is in A334556.

Conjecture: Records occur at 1 and at 2^n + 1.

Conjecture: a(n) = 1 if and only if n is a power of two.

Links

Peter Kagey, Table of n, a(n) for n = 1..8191 (values less than 2^13)

MathOverflow user DSM, Number triangle

Index entries for sequences related to binary expansion of n

Example

For n = 19, the binary expansion of 19 is 10011_2, and the XOR-triangle with first row generated from the binary expansion of 19 is:
  1 0 0 1 1
   1 0 1 0
    1 1 1
     0 0
      0
Reading the right side of the triangle starting from the upper-right corner gives 10100 which is the binary representation of 20 = a(19).

Prog

(PARI) a(n) = {my(b=binary(n), v=vector(#b)); v[#b] = b[#b]; for (n=1, #b-1, b = vector(#b-1, k, bitxor(b[k], b[k+1])); v[#b] = b[#b]; ); fromdigits(Vecrev(v), 2); } \\ Michel Marcus, May 08 2020

Crossrefs

Cf. A334556, A334591, A334592, A334593, A334594, A334596.

Sequence in context: A232467 A131449 A289869 * A350684 A124443 A077172

Adjacent sequences: A334592 A334593 A334594 * A334596 A334597 A334598

Keyword

nonn,base,look

Author

Peter Kagey, May 07 2020

Status

approved