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

Author

N. J. A. Sloane, Sep 01 2019

Keywords

• nonn
• more

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.

Crossrefs

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

Programs

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

Formula

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

Extensions

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

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