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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
5, 7, 29, 47, 119, 699, 1407, 4911, 18971, 46803, 119951, 363209, 1276197, 3722389, 19973297, 73605289, 183273481, 390720475, 1671075265, 4541314567, 22107473795, 44810965685, 172567099183, 617945607281, 1835952288687, 3938674815741, 19847928172101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

All terms are odd; see Formula section. - Jon E. Schoenfield, Mar 29 2021

LINKS

Table of n, a(n) for n=1..27.

FORMULA

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

EXAMPLE

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

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.

CROSSREFS

Cf. A000796, A280533.

Sequence in context: A018776 A104683 A153121 * A070153 A293943 A171619

Adjacent sequences:  A280923 A280924 A280925 * A280927 A280928 A280929

KEYWORD

nonn,base,more

AUTHOR

Rick L. Shepherd, Jan 10 2017

EXTENSIONS

a(13)-a(27) from Jon E. Schoenfield, Mar 28 2021

STATUS

approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)