1,6

I define the peak-trough transform b(n) of sequence a(n) as follows. If a(n) is greater than both of its immediate neighbors, b(n) is defined as the largest k such that a(n) is greater than its k nearest neighbors 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 neighbors, b(n) is defined as -k, where k is the largest k such that a(n) is smaller than its k nearest neighbors 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).

Cf. A001221, A101932.

Sequence in context: A069531 A035677 A143276 this_sequence A089313 A052998 A114516

Adjacent sequences: A101938 A101939 A101940 this_sequence A101942 A101943 A101944

sign

N. Fernandez (primeness(AT)borve.org), Dec 22 2004