This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A296870 #11 Jan 22 2023 20:51:16 %S A296870 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26, %T A296870 27,28,29,30,31,32,33,34,35,36,42,43,44,45,46,47,50,51,52,53,57,58,59, %U A296870 64,65,71,72,78,79,84,85,86,87,88,89,93,94,95,100,101 %N A296870 Numbers whose base-6 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments. %C A296870 A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296870-A296872 partition the natural numbers. See the guides at A296882 and A296712. %H A296870 Clark Kimberling, <a href="/A296870/b296870.txt">Table of n, a(n) for n = 1..10000</a> %e A296870 The base-6 digits of 101 are 2,4,5; here #(pits) = 0 and #(peaks) = 0, so 101 is in the sequence. %t A296870 z = 200; b = 6; %t A296870 d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]]; %t A296870 Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296870 *) %t A296870 Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296871 *) %t A296870 Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296872 *) %Y A296870 Cf. A296882, A296712, A296871, A296872. %K A296870 nonn,base,easy %O A296870 1,2 %A A296870 _Clark Kimberling_, Jan 09 2018