It is shown that for any integers k≥2, q≥2k and N≥k+q+2 there exists a real solvable Lie algebra of rank one with a maximal torus of derivations t possessing the eigenvalue spectrum spec(t)=1,2,⋯,k,q,q+1⋯,N and a nilradical of nilpotence index N−k and characteristic sequence (N−k,1k).
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