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

1,2

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, Youtube

Michael S. Branicky, Comma-Predecessor Theorem

Prog

(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

Crossrefs

Cf. A121805, A337338, A367614.

Sequence in context: A110029 A302027 A302028 * A023779 A367611 A247812

Adjacent sequences: A367597 A367598 A367599 * A367601 A367602 A367603

Keyword

nonn,base

Author

Giovanni Resta, Nov 23 2023

Status

approved