A367600 Numbers that are not the comma-successor of any number.

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, 60, 62, 63, 64, 65, 70, 74, 75, 76, 80, 86, 87, 90, 98, 200, 300, 400, 500, 600, 700, 800, 900, 2000, 3000, 4000, 5000, 6000, 7000

Offset: 1

Author

Giovanni Resta, Nov 23 2023

Keywords

• nonn
• base

Comments

These are the positive integers that do not appear in A367338.

All terms > 98 are of the form c*10^i for i >= 2 and 2 <= c <= 9; see proof in links. - Michael S. Branicky, Nov 28 2023

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..110 (all terms < 10^9)
• 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
• Michael S. Branicky, Comma-Predecessor Theorem

Crossrefs

Cf. A121805, A337338, A367614.

Programs

Python

from itertools import count, islice
def A367338(n):
    nn = n + 10*(n%10)
    return next((nn+y for y in range(1, 10) if str(nn+y)[0] == str(y)), -1)
def agen():
    A367338_set = set()
    for n in count(1):
        A367338_set.add(A367338(n))
        if n not in A367338_set:
            yield n
        # A367338_set.discard(n-100) # uncomment if memory is an issue
print(list(islice(agen(), 86))) # Michael S. Branicky, Nov 28 2023