# 整数

“上帝创造了整数，其他一切都是人类的工作。”克罗内克

{..., –20, –19, –18, –17, –16, –15, –14, –13, –12, –11, –10, –9, –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...}

A类整数的置换，使用公式

${\显示样式a（n）=（-1）^{n}\left\lfloor{\frac{n+1}{2}\right\rfloor，\quad n\geq 0，\，}$

{0, –1, 1, –2, 2, –3, 3, –4, 4, –5, 5, –6, 6, –7, 7, –8, 8, –9, 9, –10, 10, –11, 11, –12, 12, –13, 13, –14, 14, –15, 15, –16, 16, –17, 17, –18, 18, –19, 19, –20, 20, –21, 21, –22, 22, ...}

## 零、单位、素数和合成

A类单元（即。可逆整数)既不是质数也不是复合数，因为它可以被任何非非一致性整除，因此的单位-1和1${\displaystyle\scriptstyle\mathbb{Z}\，}$既不是质数也不是复合数。

• 负复合数: {−4, −6, −8, −9, −10, −12, −14, −15, −16, −18, −20, −21, −22, −24, −25, −26, −27, −28, ...} (−1 ×A002808号)
• 负素数: {−2, −3, −5, −7, −11, −13, −17, −19, −23, −29, −31, −37, −41, −43, −47, -53, -59, ...} (−1 ×A000040型)
• 负极单元: {−1}
• : {0}
• 阳性单位: {1}
• 正素数: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, ...} (A000040型)
• 正复合数: {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, ...} (A002808号)

## 奇偶整数

A005843号偶数[非负整数]：${\显示样式\脚本样式a（n）\，=\，2n\，}$.

{0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, ...}

A005408号奇数[非负整数]：${\显示样式\脚本样式a（n）\，=\，2n+1 \，}$.

{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, ...}