A241203 a(n) = floor(5^n/4^(n-1)).

5, 6, 7, 9, 12, 15, 19, 23, 29, 37, 46, 58, 72, 90, 113, 142, 177, 222, 277, 346, 433, 542, 677, 847, 1058, 1323, 1654, 2067, 2584, 3231, 4038, 5048, 6310, 7888, 9860, 12325, 15407, 19259, 24074, 30092, 37615, 47019, 58774, 73468, 91835, 114794, 143492, 179366, 224207, 280259

Offset: 1

Author

Kival Ngaokrajang, Aug 08 2014

Keywords

• nonn
• easy

Comments

a(n) is the curvature (rounded down) of circles inscribed in minor segment where chord length equal to sagitta length starting from a unit circle, the next iterations are nested down at scale factor 4/5. The curvature of circles inscribed in major segment would be A065565: floor((5/4)^n). See illustrations.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Kival Ngaokrajang, Illustrations of initial terms

Crossrefs

Cf. A065565.

Programs

Magma

[Floor(4*(5/4)^n): n in [1..60]]; // G. C. Greubel, Jun 07 2023

Mathematica

Floor[4*(5/4)^Range[60]] (* G. C. Greubel, Jun 07 2023 *)

PARI

for(n=1,100,print1(floor(5^n/4^(n-1)),", "))

SageMath

[(5^n//4^(n-1)) for n in range(1,61)] # G. C. Greubel, Jun 07 2023

Formula

a(n) = floor(5^n/4^(n-1)), n >= 1.