A354948 - OEIS

%I #97 Jul 02 2022 09:31:21

%S 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,

%T 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,

%U 0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,1

%N 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.

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

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Non-integer_base_of_numeration">Non-integer base of numeration</a>

%e Array begins:

%e       k=1  2  3  4  5  6  7  8

%e   n=1:  0, 0, 0, 0, 0, 0, 0, 0,

%e   n=2:  0, 1, 0, 0, 1, 0, 0, 1,

%e   n=3:  0, 0, 1, 0, 1, 0, 0, 0,

%e   n=4:  0, 0, 1, 0, 0, 0, 0, 0,

%e   n=5:  0, 0, 0, 1, 0, 0, 1, 0,

%e   n=6:  0, 0, 0, 1, 0, 0, 0, 0,

%e   n=7:  0, 0, 0, 0, 1, 0, 1, 0,

%e   n=8:  0, 0, 0, 0, 1, 0, 1, 0,

%e Row n=6 is 1/6 = .0001000010101001... in base phi.

%o (PARI)

%o phi = quadgen(5);

%o T(n, k) = {

%o     if (n == 1, 0,

%o         my (t = 1/n, d = 0);

%o         for (i=1, k,

%o             t = t * phi;

%o             t -= (d = t >= 1));

%o         d)};

%Y Cf. A001622, A173857, A173858.

%Y Cf. A355202 (binary).

%K base,nonn,tabl

%O 1

%A _Chittaranjan Pardeshi_, Jun 12 2022