cp's OEIS Frontend

A280926 Least k such that the first n digits of the decimal expansion of the ratio of the perimeter of a regular k-gon to its diameter match those of Pi.

%I A280926 #23 Apr 01 2021 14:57:38
%S A280926 5,7,29,47,119,699,1407,4911,18971,46803,119951,363209,1276197,
%T A280926 3722389,19973297,73605289,183273481,390720475,1671075265,4541314567,
%U A280926 22107473795,44810965685,172567099183,617945607281,1835952288687,3938674815741,19847928172101
%N A280926 Least k such that the first n digits of the decimal expansion of the ratio of the perimeter of a regular k-gon to its diameter match those of Pi.
%C A280926 By definition, the diameter of a regular k-gon is the length of its longest diagonal.
%C A280926 All terms are odd; see Formula section. - _Jon E. Schoenfield_, Mar 29 2021
%F A280926 a(n) = 1 + 2*floor((1/2)*(1 + sqrt((Pi^3/24)/(Pi-floor(Pi*10^(n-1))/10^(n-1))))). - _Jon E. Schoenfield_, Mar 28 2021
%e A280926 An equilateral triangle (k=3) has no diagonals, and a square (k=4) has perimeter/diameter = sqrt(8) = 2.828427..., but a regular pentagon (k=5) has perimeter/diameter = (5/2)*(sqrt(5) - 1) = 3.090169..., whose first digit (3) matches that of Pi = 3.141592..., so a(1)=5. - _Jon E. Schoenfield_, Mar 31 2021
%e A280926 This ratio for a regular 7-gon (heptagon) is 3.115293... (A280533), where 3.1 equals the first two digits of Pi's decimal expansion. Because the first two digits are not 3.1 for k < 7, a(2) = 7.
%Y A280926 Cf. A000796, A280533.
%K A280926 nonn,base,more
%O A280926 1,1
%A A280926 _Rick L. Shepherd_, Jan 10 2017
%E A280926 a(13)-a(27) from _Jon E. Schoenfield_, Mar 28 2021