A367356 Length of base-3 Commas sequence when started at n.

17, 5, 2, 1, 16, 164, 490, 163, 4, 3, 489, 15, 14, 2, 162, 161, 13, 1472, 488, 1471, 160, 1, 159, 487, 12, 486, 1470, 1469, 11, 158, 157, 1468, 485, 484, 156, 10, 9, 483, 1467, 1466, 8, 155, 154, 1465, 482, 481, 153, 7, 6, 480, 1464, 1463, 5, 41, 152, 40, 1462, 479, 1461, 151, 4, 150, 478, 39, 477, 3, 1460, 2, 38, 149, 37, 1459, 476, 1458, 148, 1, 147, 475, 36, 474, 1457, 1456, 35, 146, 145, 1455, 473, 472, 144, 34, 33, 471, 1454, 1453, 32, 143, 142, 1452, 470, 469

Offset

1,1

Comments

a(n) = 1 for n = 4, 22, 76, ... (the numbers 222...2211 in ternary)

We now know that a(n) is finite for all n.

Links

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

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Example

For a(1) = 17, see A367355, which has 17 terms.

Prog

(Python)
from itertools import islice
from sympy.ntheory.factor_ import digits
def a(n, b=3): # generator of terms
    an, y, c = n, 1, 0
    while y < b:
        an, y, c = an + b*(an%b), 1, c+1
        while y < b:
            if str(digits(an+y, b)[1]) == str(y):
                an += y
                break
            y += 1
    return c
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Nov 18 2023

Crossrefs

Cf. A121805, A330128, A367355.

Sequence in context: A040279 A070718 A040277 * A196924 A109215 A254070

Adjacent sequences: A367353 A367354 A367355 * A367357 A367358 A367359

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 18 2023

Status

approved