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Peak-trough transform of the omega sequence (A001221).
2

%I #11 May 26 2023 08:49:44

%S 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,-1,11,

%T 0,0,0,0,0,0,-3,0,0,0,-1,11,-1,0,0,0,-1,1,-1,0,0,0,-3,0,0,0,0,0,-1,5,

%U -1,0,0,-2,0,3,-2,0,0,3,-1,1,-1

%N Peak-trough transform of the omega sequence (A001221).

%C I define the peak-trough transform (b(n)) of sequence (c(n)) as follows. If c(n) is greater than both of its immediate neighbors, b(n) is defined as the largest k <= n-1 such that c(n) is greater than its k nearest neighbors both before and after it in the sequence. (c(n) is said to be a k-peak of the sequence). If c(n) is smaller than both of its immediate neighbors, b(n) is defined as -k, where k is the largest k <= n-1 such that c(n) is smaller than its k nearest neighbors both before and after it in the sequence. (c(n) is said to be a k-trough of the sequence). Otherwise, b(n) is 0. (Note difference between a k-peak and a k-apex as defined by Joseph L. Pe in A076759).

%Y Cf. A001221, A023188, A076759, A101932.

%K sign

%O 1,6

%A _Neil Fernandez_, Dec 22 2004

%E Corrected by _Peter Munn_, May 26 2023