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%I #50 Feb 07 2024 13:21:43
%S 11,23,59,41,51,62,83,13,43,74,14,55,5,55,5,56,16,77,47,18,99,89,71,
%T 81,91,1,11,21,31,41,51,61,71,81,91,1,11,21,31,41,51,61,71,82,2,22,42,
%U 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
%N First differences of "commas" sequence A121805.
%C 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.
%C The first differences of this sequence (i.e., the second differences of A121805) fall into the range [-90,90] for the first 99999 terms.
%C More generally, for a commas sequence in base b, the first differences are <= b^2 - 1. - _Michael S. Branicky_, Nov 16 2023.
%H Michael S. Branicky, <a href="/A366487/b366487.txt">Table of n, a(n) for n = 1..20000</a> (terms 1..1000 from N. J. A. Sloane)
%H Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, <a href="http://arxiv.org/abs/2401.14346">arXiv:2401.14346</a>, <a href="https://www.youtube.com/watch?v=_EHAdf6izPI">Youtube</a>
%H Michael S. Branicky, <a href="/A366487/a366487.txt">Table of n, a(n) for n = 1..100000</a>
%H Michael S. Branicky, <a href="/A366487/a366487.png">Graph of entire sequence</a>
%o (Python)
%o from itertools import islice
%o def agen(): # generator of terms
%o an, y = 1, 1
%o while y < 10:
%o prevan = an
%o an, y = an + 10*(an%10), 1
%o while y < 10:
%o if str(an+y)[0] == str(y):
%o an += y
%o break
%o y += 1
%o yield an - prevan
%o print(list(islice(agen(), 99))) # _Michael S. Branicky_, Nov 12 2023
%Y Cf. A121805.
%Y For the numbers missing from this sequence see A367349.
%K nonn,fini,base
%O 1,1
%A _N. J. A. Sloane_, Nov 12 2023