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A324787 Index of n-th low point in A022837. 5
2, 5, 12, 29, 78, 199, 508, 1355, 3592, 9589, 25752, 70579, 194228, 539961, 1507602, 4228745, 11913940, 33690443, 95581182, 272003821, 776082524, 2219823175, 6363074656 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..22.

Rémy Sigrist, PARI program for A324787


Riecaman := proc(a, s, M)

# Start with s, add or subtract a[n], get M terms. If a has w terms, can get M=w+1 terms.

local b, M2, n, t;

if whattype(a) <> list then ERROR("First argument should be a list"); fi;

if a[1]=0 then ERROR("a[1] should not be zero"); fi;

M2 := min(nops(a), M-1);

b:=[s]; t:=s;

for n from 1 to M2 do

   if a[n]>t then t:=t+a[n] else t:=t-a[n]; fi; b:=[op(b), t]; od:

b; end;

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;

# if a[1] a low point?


   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

# if 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;

p0:=[seq(ithprime(n), n=1..100001)]:

q1:=Riecaman(p0, 1, 100000):

blocks(q1, 0); # produces [the present sequence, A324788, A324789]


(PARI) See Links section.


Cf. A022837, A324788, A324789, A324790.

If the basic sequence (A022837) began with 0 instead of 1 we would get A008348, A309226, A324782, A324783, A309225.

Sequence in context: A152171 A132807 A261234 * A333888 A228516 A101411

Adjacent sequences:  A324784 A324785 A324786 * A324788 A324789 A324790




N. J. A. Sloane, Sep 04 2019


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

a(12)-a(22) from Rémy Sigrist, Oct 18 2020



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Last modified September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)