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Expansion of the Shape of Numbers

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Document pages: 18 pages

Abstract: This article extends the concept of the shape of numbers. Originally, a shape was defined as [1, K1, K2, ···], 1K1K2Ki∈N. In this paper, the domain of a shape is extended from N to Z, the low bound is extended from 1 to Z, and KiKi+1, Ki=Ki+1, Ki>Ki+1 are allowed, which prove that they can be calculated with the similar form (T0+K0)(T1+K1)(T2+K2) ···. In this way, a lot of calculation formulas can be obtained. At the end, the form is obtained to calculate K1x···xKM+(L+K1)x···x(L+KM)+(2L+K1)x···x(2L+KM)+(3L+K1)x···x(3L+KM)+···.

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