规定:正整数n的“H运算”是:①当n为奇数时,H=3n+13;②当n为偶数时,H=nx1/2x1/2……(其中H为奇数)

3个回答

  • (1)

    H1 = 784

    H2 = 49

    H3 = 160

    H4 = 5

    H5 = 28

    H6 = 7

    H7 = 34

    H8 = 17

    H9 = 64

    H10 = 1

    H11 = 16

    H12 = 1

    H13 = 16

    ……

    从第10次运算往后,都是1、16、1、16的循环.

    (257 - 10 )÷ 2 余1,因此H257 = 16

    (2)

    显然,3A + 13 = A×2^M

    当M = 1时,3A + 13 = 2A,解得A = -13(舍弃)

    当M = 2时,3A + 13 = 4A,解得A = 13

    当M = 3时,3A + 13 = 8A,解得A = 13/5(舍弃)

    当M = 4时,3A + 13 = 16A,解得A = 1

    当M > 4时,A = 13/(2^M - 3),这个分母显然大于13,A必小于1,不可能有解.

    综上,A = 13或1.

    也就是:

    输入1时,H1 = 16,H2 = 1,H3 = 16,H4 = 1……

    输入13时,H1 = 52,H2 = 13,H3 = 52,H4 = 13……