On Sum Sets of Sidon Sets, 1. Original Research Article

A (finite or infinite) set image of positive integers is said to be a Sidon set if the sums a + a′ with a set membership, variant image, a′ set membership, variant image, a ≤ a′ are distinct. Denote the sum set image + image of a Sidon set image by imageimage = {s1, s2, ...}. The size of the gaps si + 1 − si, the length of the blocks of consecutive integers in imageimage, and the number of solutions of s ≤ n, s − d negated set membership image, s set membership, variant image are studied.