A309226 Index of n-th low point in A008348 (see Comments for definition).

0, 3, 8, 21, 56, 145, 366, 945, 2506, 6633, 17776, 48521, 133106, 369019, 1028404, 2880287, 8100948, 22877145, 64823568, 184274931, 525282740, 1501215193, 4299836186, 12340952049, 35486796312, 102220582465, 294917666854, 852123981581, 2465458792768

Offset

0,2

Comments

A "low point" in a sequence is a term which is less than the previous term (this condition is skipped for the initial term) and which is followed by two or more increases.

This concept is useful for the analysis of sequences (such as A005132, A008344, A008348, A022837, A076042, A309222, etc.) which have long runs of terms which alternately rise and fall.

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = A135025(n-1)-1.

Maple

blocks := proc(a, S) local b, c, d, M, L, n;
# Given a list a, whose leading term has index S, return [b, c, d], where b lists the indices of the low points in a, c lists the values of a at the low points, and d lists the length of runs between the low points.
b:=[]; c:=[]; d:=[]; L:=1;
# is a[1] a low point?
   n:=1;
   if( (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
   b:=[op(b), n+S-1]; c:=[op(c), a[n]]; d:=[op(d), n-L]; L:=n; fi;
for n from 2 to nops(a)-2 do
# is a[n] a low point?
   if( (a[n-1]>a[n]) and (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
   b:=[op(b), n+S-1]; c:=[op(c), a[n]]; d:=[op(d), n-L]; L:=n; fi; od;
[b, c, d]; end;
# Let a := [0, 2, 5, 0, 7, 18, 5, 22, 3, 26, 55, 24, ...]; be a list of the first terms in A008348
blocks(a, 0)[1]; # the present sequence
blocks(a, 0)[2]; # A324782
blocks(a, 0)[3]; # A324783

Crossrefs

Cf. A005132, A008344, A008348, A022837, A076042, A135025, A309222, A324782, A324783.

Sequence in context: A072632 A001671 A360054 * A278616 A278615 A090413

Adjacent sequences: A309223 A309224 A309225 * A309227 A309228 A309229

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 01 2019

Extensions

a(17)-a(28) from Giovanni Resta, Oct 02 2019

Modified definition to make offset 0. - N. J. A. Sloane, Oct 02 2019

Status

approved