A296904 - OEIS

%I #13 Jan 21 2023 02:23:09

%S 401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,

%T 418,419,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,

%U 816,817,818,819,822,823,824,825,826,827,828,829,830,831,832,833,834,835

%N Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

%C 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 A296903..A296905 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296904/b296904.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-20 digits of 328822 are 2,1,2,1,2; here #(pits) = 2 and #(peaks) = 1, so 328822 is in the sequence.

%t z = 200; b = 20;

%t d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296903 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296904 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296905 *)

%Y Cf. A296882, A296712, A296904, A296905.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018