# peak-trough transform

Neil Fernandez primeness at borve.demon.co.uk
Wed Dec 22 15:11:57 CET 2004

```%S A101941 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 1, -1,
0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -1,
3, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 3, -1, 0, 0,
-1, 0, 3, -1, 0, 0, 3, -1, 1, -1
%N A101941 Peak-Trough Transform of the omega sequence (A001221)
%C A101941 I define the Peak-Trough Transform b(n) of sequence a(n) as
follows. If a(n) is greater than both of its immediate neighbours, b(n)
is defined as the largest k such that a(n) is greater than its k nearest
neighbours both before and after it in the sequence. (a(n) is said to be
a k-peak of the sequence). If a(n) is smaller than both of its immediate
neighbours, b(n) is defined as -k, where k is the largest k such that
a(n) is smaller than its k nearest neighbours both before and after it
in the sequence. (a(n) is said to be a k-trough of the sequence).
Otherwise, a(n) is 0. (Note difference between a k-peak and a k-apex as
defined by Joseph L. Pe in A076759)

%S A101949 0, 0, 0, 1, -1, 1, -1, 0, 1, -1, 1, 0, -1, 0, 0, 0, -1, 1, 0,
-1, 1, -1, 0, 3, 0, -1, 1, -1, 0, 3, -1, 1, -1, 3, -1, 0, 0, -1, 0, 0, -
1, 3, -1, 1, -1, 0, 0, 0, -1, 0, 1, -1, 3, 0, 0, 0, -1, 1, 0, -1, 0, 3,
0, -3, 0, 3, -1, 1, -3, 0, 0
%N A101949 Peak-Trough Transform of the prime-gap sequence (A001223)

--
Neil Fernandez

```