The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242394 Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (0,0). 4
 6, 18, 30, 42, 54, 66, 66, 102, 114, 126, 138, 150, 150, 162, 198, 210, 222, 234, 222, 270, 258, 294, 306, 318, 330, 330, 366, 354, 390, 402, 390, 426, 450, 462, 450, 486, 474, 486, 510, 546, 558, 546, 558, 594, 606, 630, 642, 654, 618, 678, 690, 690, 726, 738, 750, 738, 750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For all n, there are at least 6 points where the transit of circumference occurs exactly at the corners. The rare case is when the transit occurs at 2 corners of a triangle, i.e., at n = 1, 13, 181, 35113, ... , (A001570(n)). The pattern repeats itself at every Pi/3 sector along the circumference. The triangle count per half sector by rows can be arranged as an irregular triangle as shown in the illustration. The rows count (A242396) is equal to the case centered at (1/2,0), A242395. LINKS Kival Ngaokrajang, Illustration of initial terms Kival Ngaokrajang, Illustration for rare cases PROG (Small Basic) For n =1 To 100   r6=n*math.Sin(30*Math.Pi/180)/(Math.Power(3, 0.5)/2)   r6a=math.Round(r6)   If r6-math.Floor(r6) >0.5 Then     last=1   Else     last=2   EndIf   'find corner intersecting points-----------------------     k=0     ic=0     h=Math.Power(1-0.5*0.5, 0.5)     c=math.Floor(n/h)     For i = h To c Step h       For j = 0.5 To n Step 0.5         r=Math.Power(i*i+j*j, 0.5)         If r = n Then           k=k+1         EndIf       EndFor     EndFor     if k > 1 then       ic=math.Floor(k/3)     EndIf   '------------------------------------------------------   a=0   b=0   For ii=1 To r6a     If ii=1 Then       a=a+1     Else       If ii = r6a Then         a=a+last       Else         a=a+2       EndIf     EndIf     b=a   EndFor   if n =1 then     aa = 1   Else     aa =1*(a-2*ic)*2+1   endif   TextWindow.Write(6*aa+", ") EndFor CROSSREFS Cf. A001570, A242118. Sequence in context: A077660 A240991 A304050 * A030568 A017593 A335908 Adjacent sequences:  A242391 A242392 A242393 * A242395 A242396 A242397 KEYWORD nonn AUTHOR Kival Ngaokrajang, May 13 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 6 18:38 EDT 2021. Contains 343586 sequences. (Running on oeis4.)