A367600 -id:A367600 - cp's OEIS frontend

A367614 a(n) is the unique k such that n is the comma-successor of k, or -1 if k does not exist.

-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 20, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, 30, 21, 12, 3, -1, -1, -1, -1, -1, -1, -1, 40, 31, 22, 13, 4, -1, -1, -1, -1, -1, -1, 50, 41, 32, 23, 14, -1, 5, -1, -1, -1, -1, 60, 51, 42, 33, -1, 24, 15, 6, -1, -1, -1, 70, 61, 52, -1, 43, 34, 25, 16, 7

Offset: 1

N. J. A. Sloane, Dec 16 2023

If k exists, it could be called the comma-predecessor of n.
a(n) is the unique k such that A367338(k) = n, or -1.
a(n) = -1 iff n is in A367600.

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

Cf. A121805, A367600, A367338.

def a(n):
    y = int(str(n)[0])
    x = (n-y)%10
    k = n - y - 10*x
    kk = k + 10*x + y-1
    return k if k > 0 and int(str(kk)[0]) != y-1 else -1
print([a(n) for n in range(1, 86)]) # Michael S. Branicky, Dec 16 2023

A367611 Numbers that are not the comma-child of any positive number.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 43, 49, 50, 51, 52, 53, 54, 62, 63, 64, 65, 74, 75, 76, 86, 87, 98

Offset: 1

Michael S. Branicky and N. J. A. Sloane, Dec 15 2023

A subsequence of A367600.
This 50-term sequence was found by David W. Wilson in 2007. See the Eric Angelini link.
See A367338 for definition of comma-child.

Eric Angelini, The Commas Sequence, Message to Sequence Fans, Sep 06 2016. [Cached copy, with permission]
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, Fibonacci Quarterly 62:3 (2024), 215-232.
Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, Local copy.
N. J. A. Sloane, Eric Angelini's Comma Sequence, Experimental Math Seminar, Rutgers Univ., January 18, 2024, Youtube video; Slides

Cf. A121805, A367600.

A367612 gives the complement.

def ok(n): y = int(str(n)[0]); x = (n-y)%10; return n - y - 10*x < 1
print([k for k in range(1, 99) if ok(k)]) # Michael S. Branicky, Dec 15 2023

cp's OEIS Frontend

A367614 a(n) is the unique k such that n is the comma-successor of k, or -1 if k does not exist.

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