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

0,3

Comments

The initial number counts as iteration 1.

Links

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

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.

Prog

(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

Crossrefs

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

Sequence in context: A243434 A265416 A199953 * A076039 A280580 A288872

Adjacent sequences: A364679 A364680 A364681 * A364683 A364684 A364685

Keyword

nonn

Author

Chai Wah Wu, Aug 02 2023

Status

approved