On Finite Pseudorandom Binary Sequences, V.On (nα) and (n2α) Sequences

 Let k be a positive integer and α be a real number, and for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} if the fractional part of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} is <1/2 and en=−1 if it is ≥1/2. The pseudorandom properties of the sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} are studied. As measures of pseudorandomness, the regularity of the distribution relative to arithmetic progressions and the correlation are used. Here the special cases k=1 and k=2 are studied (while the case k>2 will be studied in the sequel).