A378562 a(n) is the number of steps to reach 1 by reversing digits of n in the lowest base where reversal reduces the number.

0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 4, 3, 3, 1, 5, 2, 4, 2, 2, 5, 5, 2, 5, 4, 1, 3, 6, 4, 4, 1, 5, 6, 4, 2, 5, 6, 5, 2, 6, 3, 5, 5, 3, 7, 7, 2, 5, 5, 6, 4, 6, 2, 7, 3, 6, 6, 8, 4, 8, 5, 2, 1, 9, 6, 7, 6, 6, 6, 8, 2, 5, 7, 6, 6, 9, 7, 7, 2, 7, 6, 7, 3, 5, 7, 8

Offset

1,6

Comments

The procedure is guaranteed to reach 1 because n in base n is 10, and its reversal is 01 = 1.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Michael S. Branicky, Alternate Python programs for A378562

Example

For n = 13, the a(13) = 4 steps in the trajectory to 1 are 13 -> 11 -> 7 -> 5 -> 1.

Prog

(Python) # see links for other versions
from functools import cache
from sympy.ntheory import digits
def fd(t, b): return sum(t[-1-i]*b**i for i in range(len(t)))
def f(n): return next(fd(r, b) for b in range(2, n+1) if (s:=digits(n, b)[1:]) > (r:=s[::-1]))
@cache
def a(n): return 0 if n == 1 else 1 + a(f(n))
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Dec 01 2024

Crossrefs

Cf. A004086, A030101.

Sequence in context: A305825 A366780 A324029 * A334046 A136605 A380367

Adjacent sequences: A378559 A378560 A378561 * A378563 A378564 A378565

Keyword

nonn,base,easy

Author

Asier Rodriguez Escalante, Nov 30 2024

Status

approved