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A362942 Partial sums of A229037.

%I A362942 #25 Sep 27 2023 15:08:02
%S A362942 1,2,4,5,6,8,10,14,18,19,20,22,23,24,26,28,32,36,38,42,46,51,56,64,69,
%T A362942 74,83,84,85,87,88,89,91,93,97,101,102,103,105,106,107,109,111,115,
%U A362942 119,121,125,129,134,139,147,152,157,166,175,179,183,188,193
%N A362942 Partial sums of A229037.
%H A362942 Michael S. Branicky, <a href="/A362942/b362942.txt">Table of n, a(n) for n = 1..100000</a> (using b-file in A229037)
%H A362942 N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: <a href="https://vimeo.com/866583736?share=copy">Video</a>, <a href="http://neilsloane.com/doc/EMSep2023.pdf">Slides</a>, <a href="http://neilsloane.com/doc/EMSep2023.Updates.txt">Updates</a>. (Mentions this sequence.)
%t A362942 a[1] = 1; a[n_] := a[n] = Block[{z = 1}, While[Catch[Do[If[z == 2*a[n - k] - a[n - 2*k], Throw@ True], {k, Floor[(n - 1)/2]}]; False], z++]; z]; Accumulate@ Array[a, 120] (* _Michael De Vlieger_, Sep 12 2023, after _Giovanni Resta_ at A229037 *)
%o A362942 (Python)
%o A362942 from itertools import count, islice
%o A362942 def A362942_gen(): # generator of terms
%o A362942     blist, c = [], 0
%o A362942     for n in count(0):
%o A362942         i, j, b = 1, 1, set()
%o A362942         while n-(i<<1) >= 0:
%o A362942             b.add((blist[n-i]<<1)-blist[n-2*i])
%o A362942             i += 1
%o A362942             while j in b:
%o A362942                 j += 1
%o A362942         blist.append(j)
%o A362942         yield (c:=c+j)
%o A362942 A362942_list = list(islice(A362942_gen(),30)) # _Chai Wah Wu_, Sep 12 2023
%Y A362942 Cf. A003002, A229037.
%K A362942 nonn
%O A362942 1,2
%A A362942 _N. J. A. Sloane_, Sep 12 2023