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A296765 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

%I A296765 #11 Jan 22 2023 20:49:34
%S A296765 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 A296765 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A296765 50,51,52,53,54,55,56,57,58,59,61,122,183,244,305,366
%N A296765 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
%C A296765 A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296762-A296764 partition the natural numbers. This sequence differs from A262065; see the example.  For a guide to related sequences, see A296712.
%H A296765 Clark Kimberling, <a href="/A296765/b296765.txt">Table of n, a(n) for n = 1..10000</a>
%e A296765 The base-60 digits of 13406581 are 1, 2, 4, 3, 1; here #(rises) = 2 and #(falls) = 2, so 13406581 is in the sequence.  This sequence is not A262065, as not all the terms in this sequence are palindromes.
%t A296765 z = 200; b = 60; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t A296765 Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296765 *)
%t A296765 Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296766 *)
%t A296765 Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296767 *)
%Y A296765 Cf. A296766, A296767, A296712, A262065.
%K A296765 nonn,base,easy
%O A296765 1,2
%A A296765 _Clark Kimberling_, Jan 08 2018