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 A121546 a(n) = dimension of the space in which the sphere of radius n is of maximum volume. 0
 5, 24, 56, 100, 156, 225, 307, 401, 508, 627, 759, 904, 1061, 1231, 1413, 1607, 1815, 2035, 2267, 2512, 2770, 3040, 3323, 3618, 3926, 4246, 4579, 4925, 5283, 5654, 6037, 6433, 6841, 7262, 7696, 8142, 8601, 9072, 9556, 10052, 10561, 11083, 11617, 12163 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS John Moeller, Reasoning in Higher Dimensions: Hyperspheres, onTopology Blog, 3 March 2009. FORMULA a(n) >= 6.2835n^2 - 0.009903n - 0.9212 is a lower bound on the real value of the dimension. MAPLE N:= 10^5: # to get all terms <= N G[1]:= 2/Pi: G[2]:= 3/4: L[2]:= 0: for n from 3 to N do   G[n]:= G[n-2]*(n+1)/n;   L[n]:= floor(G[n]);   if L[n] <> L[n-1] then      A[L[n]]:= n   fi od: seq(A[i], i=1..L[N]); # Robert Israel, Jan 05 2016 MATHEMATICA vol[n_, r_]:=If[IntegerQ[n/2], (Pi^(n/2)*r^n)/(n/2)!, (Pi^((n-1)/2)*((n+1)/2)!*2^(n+1)*r^n)/(n+1)!]; dim[r_]:=Block[{d=1}, While[vol[d, r]

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Last modified October 16 06:21 EDT 2019. Contains 328048 sequences. (Running on oeis4.)