A359255 Number of steps to reach a maximum starting with n in the map x->A359194(x) (binary complement of 3n), or -1 if n goes to infinity.

0, 0, 0, 7, 8, 0, 6, 1, 2, 9, 0, 15, 28, 5, 1, 11, 12, 29, 10, 7, 8, 0, 2, 31, 4, 21, 5, 27, 2962, 1, 14, 23, 24, 2963, 22, 3, 8, 13, 6, 0, 0, 9, 0, 2961, 2, 33, 26, 11, 74, 4, 1591, 69, 20, 5, 3, 3, 34, 9, 30, 1, 16, 1, 76, 11

Offset: 0

Author

Hans Havermann, Dec 22 2022

Keywords

• nonn
• base

Comments

The corresponding maxima reached are in A359208. The indices at which zeros appear here are in A359209.

Links

• Hans Havermann, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A359194, A359207, A359208, A359209.

Programs

Mathematica

f[n_] := FromDigits[BitXor[1, IntegerDigits[3*n, 2]], 2]; Table[c=m=0; n=r=i; While[n!=0, c++; n=f[n]; If[n>r, m=c; r=n]]; m, {i, 0, 63}]

Python

def f(n): return 1 if n == 0 else (m:=3*n)^((1 << m.bit_length())-1)
def a(n):
    i, fi, m, mi = 0, n, n, 0
    while fi != 0:
        i, fi = i+1, f(fi)
        if fi > m: m, mi = fi, i
    return mi
print([a(n) for n in range(64)]) # Michael S. Branicky, Dec 22 2022