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A367619
a(n) is the most remote positive ancestor of n in the comma-child graph in base 3.
3
1, 2, 3, 3, 1, 1, 7, 1, 2, 2, 7, 1, 1, 2, 1, 1, 1, 1, 7, 1, 1, 2, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 7
OFFSET
1,2
COMMENTS
Analogous to A367617, but the calculations are done in base 3.
See A367338 for definitions of comma-child.
The sequence consists entirely of terms in {1, 2, 3, 7}. In particular, two terms, a(3) = a(4) = 3; five terms, a(2,9,10,14,22) = 2; and 490 terms are 7, ending with a(2182). All other terms a(k) are 1, since a(2183..2190) = 1 and 1 <= p(n) - n <= b^2 - 1 (= 8 for base b = 3).
LINKS
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
FORMULA
a(n) is defined as n if A367618(n) = -1, else A367618(A367618(n)).
PROG
(Python)
from functools import cache
from sympy.ntheory.factor_ import digits
def comma_parent(n, base=3): # A367618(n)
y = digits(n, base)[1]
x = (n-y)%base
k = n - y - base*x
return k if k > 0 else -1
@cache
def a(n):
cp = comma_parent(n)
if cp <= 0: return n
return a(cp)
print([a(n) for n in range(1, 88)])
CROSSREFS
KEYWORD
nonn,base
AUTHOR
STATUS
approved