A364682 Number of iterations of the "x -> sum of squares of digits of x" map (A003132) for n to converge to either 0, 1 or the 8-cycle (37,58,89,145,42,20,4,16).

1, 1, 2, 6, 1, 5, 10, 6, 6, 5, 2, 3, 6, 3, 7, 4, 1, 6, 4, 5, 1, 6, 7, 4, 2, 4, 3, 7, 4, 3, 6, 3, 4, 5, 5, 6, 9, 1, 3, 6, 2, 7, 1, 5, 5, 8, 5, 4, 7, 5, 5, 4, 4, 6, 8, 6, 3, 5, 1, 3, 10, 2, 3, 9, 5, 3, 8, 3, 3, 6, 6, 6, 7, 2, 4, 5, 3, 3, 5, 4, 6, 4, 4, 3, 7, 2

Offset: 0

Author

Chai Wah Wu, Aug 02 2023

Keywords

• nonn

Comments

The initial number counts as iteration 1.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003132, A007770, A039943, A099645, A193995.

Programs

Python

def A364682(n):
    c = 1
    while n not in {0,1,37,58,89,145,42,20,4,16}:
        n = sum((0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[ord(d)-48] for d in str(n))
        c += 1
    return c

Formula

a(n) <= A193995(n) with equality if and only if n is a Happy number (A007770).

a(n) = 1 if and only if n is in A039943.

a(n) = A099645(n)+1.