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A366487 First differences of "commas" sequence A121805. 6
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 (list; graph; refs; listen; history; text; internal format)
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, 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
KEYWORD
nonn,fini,base
AUTHOR
N. J. A. Sloane, Nov 12 2023
STATUS
approved

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Last modified May 24 13:22 EDT 2024. Contains 372773 sequences. (Running on oeis4.)