A324787 Index of n-th low point in A022837.

2, 5, 12, 29, 78, 199, 508, 1355, 3592, 9589, 25752, 70579, 194228, 539961, 1507602, 4228745, 11913940, 33690443, 95581182, 272003821, 776082524, 2219823175, 6363074656

Offset

0,1

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.

Links

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

Rémy Sigrist, PARI program for A324787

Maple

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?
   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
# 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]

Prog

(PARI) See Links section.

Crossrefs

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: A132807 A261234 A368984 * A333888 A228516 A101411

Adjacent sequences: A324784 A324785 A324786 * A324788 A324789 A324790

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 04 2019

Extensions

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

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

Status

approved