A188638 Decimal expansion of length/width of a meta-1st electrum rectangle.

1, 8, 9, 4, 0, 0, 6, 6, 5, 3, 5, 4, 7, 6, 8, 0, 5, 9, 0, 9, 4, 2, 4, 3, 8, 0, 7, 8, 8, 8, 2, 0, 5, 6, 3, 7, 8, 1, 9, 0, 4, 9, 6, 4, 5, 8, 8, 3, 9, 4, 2, 7, 3, 9, 2, 2, 1, 6, 6, 4, 2, 2, 4, 1, 9, 3, 4, 5, 2, 8, 7, 0, 8, 7, 1, 5, 9, 9, 8, 7, 0, 4, 4, 8, 1, 9, 9, 1, 1, 9, 9, 9, 9, 8, 6, 0, 3, 0, 2, 2, 8, 9, 4, 7, 8, 0, 6, 6, 4, 1, 8, 6, 7, 6, 6, 7, 1, 8, 6, 4, 5, 1, 1, 1, 2, 9, 3, 7, 6, 2

Offset: 1

Author

Clark Kimberling, Apr 06 2011

Keywords

• nonn
• cons

Comments

See A188618 for the definition of 1st electrum rectangle. Briefly, it is a rectangle such that the removal of a golden rectangle from one end leaves a silver rectangle.

Links

• Clark Kimberling, A Visual Euclidean Algorithm, The Mathematics Teacher 76 (1983) 108-109.

Crossrefs

Cf. A188618, A188619, A188639.

Programs

Mathematica

t=(1+3^(1/2))/2; r=(t+(t^2+4)^(1/2))/2
FullSimplify[r]
N[r, 130]
RealDigits[N[r, 130]][[1]]