A327856 The upper left triangular section of square array A091255, read by rows.

1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 3, 1, 5, 1, 2, 3, 2, 3, 6, 1, 1, 1, 1, 1, 1, 7, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 3, 1, 3, 3, 7, 1, 9, 1, 2, 3, 2, 5, 6, 1, 2, 3, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 2, 3, 4, 3, 6, 1, 4, 3, 6, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 2, 1, 2, 1, 2, 7, 2, 7, 2, 1, 2, 1, 14

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 rows of triangular table

Index entries for sequences operating on polynomials in ring GF(2)[X]

Formula

A(n,k) = A091255(n,k), with k in range 1 .. n.

a(A000217(n)) = n.

Example

The triangular table starts as:
  1,
  1, 2,
  1, 1, 3,
  1, 2, 1, 4,
  1, 1, 3, 1, 5,
  1, 2, 3, 2, 3, 6,
  1, 1, 1, 1, 1, 1, 7,
  1, 2, 1, 4, 1, 2, 1, 8,
  1, 1, 3, 1, 3, 3, 7, 1, 9,
  1, 2, 3, 2, 5, 6, 1, 2, 3, 10,
  ...

Prog

(PARI)
up_to = 105;
A091255sq(a, b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2), Pol(binary(b))*Mod(1, 2)))), 2);
A327856list(up_to) =  { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A091255sq(a, col))); (v); };
v327856 = A327856list(up_to);
A327856(n) = v327856[n];

Crossrefs

Cf. A000217, A091255.

Sequence in context: A050873 A324668 A128221 * A175488 A309914 A364911

Adjacent sequences: A327853 A327854 A327855 * A327857 A327858 A327859

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 28 2019

Status

approved