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

%I A309226 #21 Oct 02 2019 11:58:15
%S A309226 0,3,8,21,56,145,366,945,2506,6633,17776,48521,133106,369019,1028404,
%T A309226 2880287,8100948,22877145,64823568,184274931,525282740,1501215193,
%U A309226 4299836186,12340952049,35486796312,102220582465,294917666854,852123981581,2465458792768
%N A309226 Index of n-th low point in A008348 (see Comments for definition).
%C A309226 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.
%C A309226 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.
%F A309226 a(n) = A135025(n-1)-1.
%p A309226 blocks := proc(a,S) local b,c,d,M,L,n;
%p A309226 # 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.
%p A309226 b:=[]; c:=[]; d:=[]; L:=1;
%p A309226 # is a[1] a low point?
%p A309226    n:=1;
%p A309226    if( (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
%p A309226    b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi;
%p A309226 for n from 2 to nops(a)-2 do
%p A309226 # is a[n] a low point?
%p A309226    if( (a[n-1]>a[n]) and (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
%p A309226    b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi; od;
%p A309226 [b,c,d]; end;
%p A309226 # Let a := [0, 2, 5, 0, 7, 18, 5, 22, 3, 26, 55, 24, ...]; be a list of the first terms in A008348
%p A309226 blocks(a,0)[1]; # the present sequence
%p A309226 blocks(a,0)[2]; # A324782
%p A309226 blocks(a,0)[3]; # A324783
%Y A309226 Cf. A005132, A008344, A008348, A022837, A076042, A135025, A309222, A324782, A324783.
%K A309226 nonn,more
%O A309226 0,2
%A A309226 _N. J. A. Sloane_, Sep 01 2019
%E A309226 a(17)-a(28) from _Giovanni Resta_, Oct 02 2019
%E A309226 Modified definition to make offset 0. - _N. J. A. Sloane_, Oct 02 2019