A393501 Decimal expansion of the average dimensionless pairwise Manhattan distance between all points in a city minimizing this distance as a function of d for a symmetric boundary given by w(x) = +-(2 - |x|^d)^(1/d), |x| <= 2^(1/d).

6, 5, 0, 2, 4, 7, 6, 3, 4, 5, 5, 1, 4, 9, 0, 0, 5, 5, 7, 9, 4, 8, 7, 8, 0, 5, 5, 3, 9, 3, 1, 0, 7, 3, 4, 9, 2, 4, 3, 2, 0, 1, 7, 7, 2, 0, 5, 3, 4, 6, 6, 1, 1, 4, 0, 5, 0, 0, 8, 4, 4, 9, 8, 2, 4, 8, 4, 1, 0, 3, 2, 5, 5, 2, 5, 3, 1, 3, 5, 6, 3, 6, 3, 3, 5, 0, 4, 3, 3, 2, 3

Offset

0,1

Comments

See Bender et al. for more information.

This approximation is by 2.6*10^(-6) worse than the true minimum given by A393500.

Links

Table of n, a(n) for n=0..90.

Carl M. Bender, Michael A. Bender, Erik D. Demaine and Sándor P. Fekete, What is the optimal shape of a city?, Journal of Physics A: Mathematical and General, Volume 37, Number 1, 2014. Alternative link. (3.4, page 151)

Example

0.6502476345514900557948780553931073492432...

Prog

(PARI) {my(A(d, a)=2*a^2*gamma(1/d)^2/(d*gamma(2/d)), M(d, a)=64*a^5 * intnum(x=0, 1, x*(1-x^d)^(1/d) * intnum(u=0, x, (1-u^d)^(1/d))), f(d) = M(d, 1)*A(d, 1)^(-5/2)); f(solve(x=1.815, 1.816, f'(x)))}

Crossrefs

Cf. A193452, A393499, A393500.

Sequence in context: A200635 A197261 A393500 * A396440 A393499 A010773

Adjacent sequences: A393498 A393499 A393500 * A393502 A393503 A393504

Keyword

nonn,cons

Author

Hugo Pfoertner, Feb 17 2026

Status

approved