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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)
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
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
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
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

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Last modified April 18 15:48 EDT 2024. Contains 371780 sequences. (Running on oeis4.)