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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. 0

%I

%S 5,7,29,47,119,699,1407,4911,18971,46803,119951,363209,1276197,

%T 3722389,19973297,73605289,183273481,390720475,1671075265,4541314567,

%U 22107473795,44810965685,172567099183,617945607281,1835952288687,3938674815741,19847928172101

%N 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 By definition, the diameter of a regular k-gon is the length of its longest diagonal.

%C All terms are odd; see Formula section. - _Jon E. Schoenfield_, Mar 29 2021

%F 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 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 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 Cf. A000796, A280533.

%K nonn,base,more

%O 1,1

%A _Rick L. Shepherd_, Jan 10 2017

%E a(13)-a(27) from _Jon E. Schoenfield_, Mar 28 2021

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Last modified September 21 19:23 EDT 2021. Contains 347598 sequences. (Running on oeis4.)