A241203 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

FORMULA

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

MATHEMATICA

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

PROG

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

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

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

CROSSREFS