A366487 First differences of "commas" sequence A121805.

11, 23, 59, 41, 51, 62, 83, 13, 43, 74, 14, 55, 5, 55, 5, 56, 16, 77, 47, 18, 99, 89, 71, 81, 91, 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 1, 11, 21, 31, 41, 51, 61, 71, 82, 2, 22, 42, 62, 82, 2, 22, 42, 62, 82, 2, 22, 42, 62, 82, 2, 22, 42, 62, 82, 2, 22, 42, 63, 93, 23, 53, 83, 13, 43, 73, 3, 33, 63, 93, 23, 53, 83, 13, 43, 73, 3, 33, 63, 94, 34, 74, 14, 54, 94, 34, 74, 14, 54, 94

Offset

1,1

Comments

The record high points in this sequence are 11, 23, 59, 62, 83, 99, and they occur at terms 1, 2, 3, 6, 7, 21. Since 99 is the largest possible term, this is the full list of record high points.

The first differences of this sequence (i.e., the second differences of A121805) fall into the range [-90,90] for the first 99999 terms.

More generally, for a commas sequence in base b, the first differences are <= b^2 - 1. - Michael S. Branicky, Nov 16 2023.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..20000 (terms 1..1000 from N. J. A. Sloane)

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, Table of n, a(n) for n = 1..100000

Michael S. Branicky, Graph of entire sequence

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an, y = 1, 1
    while y < 10:
        prevan = an
        an, y = an + 10*(an%10), 1
        while y < 10:
            if str(an+y)[0] == str(y):
                an += y
                break
            y += 1
        yield an - prevan
print(list(islice(agen(), 99))) # Michael S. Branicky, Nov 12 2023

Crossrefs

Cf. A121805.

For the numbers missing from this sequence see A367349.

Sequence in context: A098100 A105967 A097473 * A081510 A068844 A139905

Adjacent sequences: A366484 A366485 A366486 * A366488 A366489 A366490

Keyword

nonn,fini,base

Author

N. J. A. Sloane, Nov 12 2023

Status

approved