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A366487 First differences of "commas" sequence A121805.

%I A366487 #52 Jan 09 2025 12:28:09
%S A366487 11,23,59,41,51,62,83,13,43,74,14,55,5,55,5,56,16,77,47,18,99,89,71,
%T A366487 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 A366487 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 A366487 First differences of "commas" sequence A121805.
%C A366487 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 A366487 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 A366487 More generally, for a commas sequence in base b, the first differences are <= b^2 - 1. - _Michael S. Branicky_, Nov 16 2023.
%H A366487 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 A366487 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>, Fibonacci Quarterly 62:3 (2024), 215-232.
%H A366487 Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, <a href="/A121805/a121805_1.pdf">The Comma Sequence: A Simple Sequence With Bizarre Properties</a>, Local copy.
%H A366487 Michael S. Branicky, <a href="/A366487/a366487.txt">Table of n, a(n) for n = 1..100000</a>
%H A366487 Michael S. Branicky, <a href="/A366487/a366487.png">Graph of entire sequence</a>
%H A366487 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=_EHAdf6izPI">Eric Angelini's Comma Sequence</a>, Experimental Math Seminar, Rutgers Univ., January 18, 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane2024.pdf">Slides</a>
%o A366487 (Python)
%o A366487 from itertools import islice
%o A366487 def agen(): # generator of terms
%o A366487     an, y = 1, 1
%o A366487     while y < 10:
%o A366487         prevan = an
%o A366487         an, y = an + 10*(an%10), 1
%o A366487         while y < 10:
%o A366487             if str(an+y)[0] == str(y):
%o A366487                 an += y
%o A366487                 break
%o A366487             y += 1
%o A366487         yield an - prevan
%o A366487 print(list(islice(agen(), 99))) # _Michael S. Branicky_, Nov 12 2023
%Y A366487 Cf. A121805.
%Y A366487 For the numbers missing from this sequence see A367349.
%K A366487 nonn,fini,base
%O A366487 1,1
%A A366487 _N. J. A. Sloane_, Nov 12 2023