For a parameter $\lambda >0$, we investigate greedy λ-energy sequences ${(a_n)}_{n=0}^{\infty }$ on the unit sphere $S^d\subset {\mathbb{R}}^{d+1}$, $d\ge 1$, satisfying the defining property that each $a_n$, $n\ge 1$, is a point where the potential ${\sum }_{k=0}^{n-1}|x-a_k{|}^{\lambda }$ attains its maximum value on $S^d$. We show that these sequences satisfy the symmetry property $a_{2k+1}=-a_{2k}$ for every $k\ge 0$. The asymptotic distribution of the sequence undergoes a sharp transition at the value $\lambda =2$, from uniform distribution ($\lambda <2$) to concentration on two antipodal points ($\lambda >2$). We investigate first-order and second-order asymptotics of the λ-energy of the first N points of the sequence, as well as the asymptotic behavior of the extremal values ${\sum }_{k=0}^{n-1}|a_n-a_k{|}^{\lambda }$. The second-order asymptotics is analyzed on the unit circle. It is shown that this asymptotic behavior differs significantly from that of N equally spaced points on the unit circle, and a transition in the behavior takes place at $\lambda =1$.

对于一个参数 $\lambda >0$，我们研究贪婪的λ -能量序列${({\mathrm{一种}}_n)}_{n=0}^{\infty }$ 在单位球面上 ${秒}^d\subset {\mathbb{电阻}}^{d+1}$, $d\ge 1$，满足定义性质，每个 ${\mathrm{一种}}_n$, $n\ge 1$, 是势能点 ${\sum }_{克=0}^{n-1}|X-{\mathrm{一种}}_{克}{|}^{\lambda }$ 达到其最大值 ${秒}^d$. 我们证明这些序列满足对称性${\mathrm{一种}}_{2克+1}=-{\mathrm{一种}}_{2克}$ 对于每个 $克\ge 0$. 序列的渐近分布在值处经历急剧转变$\lambda =2$, 从均匀分布 ($\lambda <2$) 集中在两个对映点 ($\lambda >2$）。我们研究了序列前N个点的λ能量的一阶和二阶渐近性，以及极值的渐近行为${\sum }_{克=0}^{n-1}|{\mathrm{一种}}_n-{\mathrm{一种}}_{克}{|}^{\lambda }$. 在单位圆上分析二阶渐近性。结果表明，这种渐近行为与单位圆上N 个等距点的渐近行为明显不同，行为的转变发生在$\lambda =1$.