A354948 Square array read by upwards antidiagonals: T(n,k) = k-th digit after the radix point in the expansion of 1/n in golden ratio base phi where n and k both >= 1 and phi = (1+sqrt(5))/2.

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

Offset

1

Comments

First row : since 1/1 has all zeros after radix. T(1, k) = 0 for k >= 1.

First column: since 1/phi > 1/n for n>=2; T(n, 1) = 0 for all n >= 1.

Links

Table of n, a(n) for n=1..87.

Wikipedia, Non-integer base of numeration

Example

Array begins:
      k=1  2  3  4  5  6  7  8
  n=1:  0, 0, 0, 0, 0, 0, 0, 0,
  n=2:  0, 1, 0, 0, 1, 0, 0, 1,
  n=3:  0, 0, 1, 0, 1, 0, 0, 0,
  n=4:  0, 0, 1, 0, 0, 0, 0, 0,
  n=5:  0, 0, 0, 1, 0, 0, 1, 0,
  n=6:  0, 0, 0, 1, 0, 0, 0, 0,
  n=7:  0, 0, 0, 0, 1, 0, 1, 0,
  n=8:  0, 0, 0, 0, 1, 0, 1, 0,
Row n=6 is 1/6 = .0001000010101001... in base phi.

Prog

(PARI)
phi = quadgen(5);
T(n, k) = {
    if (n == 1, 0,
        my (t = 1/n, d = 0);
        for (i=1, k,
            t = t * phi;
            t -= (d = t >= 1));
        d)};

Crossrefs

Cf. A001622, A173857, A173858.

Cf. A355202 (binary).

Sequence in context: A023971 A185014 A369036 * A330551 A346618 A079260

Adjacent sequences: A354945 A354946 A354947 * A354949 A354950 A354951

Keyword

base,nonn,tabl

Author

Chittaranjan Pardeshi, Jun 12 2022

Status

approved