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The starting point of the present paper are the papers of Schinzel [10] and of Conway, Guy, Schneeberger and Sloane [4]. Following recent papers ([1], [4], [6], [7]) a composite n is called a pseudoprime to base b if bn−1 ≡ 1 mod n. This definition does not coincide with the definition given in my book [9], where I defined (i) a pseudoprime as a composite number dividing 2 − 2, (ii) a pseudoprime with respect to b as a composite number n dividing b − b, (iii) an absolute pseudoprime as a composite number n that divides bn−b for every integer b (see also Sierpiński [12]).

Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function $l^C_x$