A234903 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A234903

a(n)*Pi is the total length of irregular spiral (center points: 1, 3, 2) after n rotations.

4, 11, 13, 20, 24, 28, 35, 37, 44, 48, 52, 59, 61, 68, 72, 76, 83, 85, 92, 96, 100, 107, 109, 116, 120, 124, 131, 133, 140, 144, 148, 155, 157, 164, 168, 172, 179, 181, 188, 192, 196, 203, 205, 212, 216, 220, 227, 229, 236, 240, 244, 251, 253, 260, 264, 268, 275, 277, 284, 288, 292, 299, 301, 308, 312, 316, 323, 325

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

OFFSET

1,1

COMMENTS

Let points 1, 3 & 2 be placed on a straight line at intervals of 1 unit. At point 1 make a half unit circle, then at point 2 make another half circle, and maintain continuity of circumferences. Continue using this procedure at points 3, 1, 2, and so on. The form of spiral is a non-expanded loop. See illustration in links.

LINKS

Table of n, a(n) for n=1..68.

Kival Ngaokrajang, Illustration of initial terms

FORMULA

G.f.: x*(4*x^4 + 7*x^3 + 2*x^2 + 7*x + 4)/((1-x)(1-x^5)) (conjectured). - Ralf Stephan, Jan 13 2014

PROG

(Small Basic)

a[1]=4

For n = 1 To 100

d1=2

m5 = math.Remainder(n+1, 5)

If m5 = 0 Or m5 = 1 Then