A367617 a(n) is the most remote positive ancestor of n in the comma-child graph.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21, 20, 10, 2, 25, 26, 27, 28, 29, 30, 31, 32, 30, 21, 1, 3, 37, 38, 39, 40, 41, 42, 43, 40, 31, 20, 13, 4, 49, 50, 51, 52, 53, 54, 50, 41, 32, 10, 14, 14, 5, 62, 63, 64, 65, 14, 51, 42, 30, 30, 2, 15, 6, 74, 75

Offset

1,2

Comments

Like A367366 but allows ancestors that are not comma-predecessors. More specifically, A367366(n) is the most remote positive ancestor of n in the comma-successor graph. See A367338 for definitions.

This sequence first differs from A367366 at n = 60.

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

a(60) = a(66) = 14, since 66 is a comma-child of 60, and 60 is a comma-child of 14, and 14 is not the comma-child of any positive number. In other words, A367616(A367616(66)) = A367616(60) = 14, and A367616(14) = -1.

Prog

(Python)
def comma_parent(n): # A367616(n)
    y = int(str(n)[0])
    x = (n-y)%10
    k = n - y - 10*x
    return k if k > 0 else -1
def a(n):
    an = n
    while (cp:=comma_parent(an)) > 0: an = cp
    return an
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Dec 18 2023

Crossrefs

Cf. A367338, A367366, A367616.

Sequence in context: A051503 A331375 A179622 * A367366 A285757 A136687

Adjacent sequences: A367614 A367615 A367616 * A367618 A367619 A367620

Keyword

nonn,base

Author

Michael S. Branicky and N. J. A. Sloane, Dec 18 2023

Status

approved