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Leading terms of successive absolute differences of the partition numbers (A000041).
2

%I #22 Sep 25 2023 19:20:38

%S 1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,1,1,1,0,0,

%T 0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,

%U 1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,1,1,1,1,1,0,1,1,1,0,67,67

%N Leading terms of successive absolute differences of the partition numbers (A000041).

%H Pontus von Brömssen, <a href="/A196251/b196251.txt">Table of n, a(n) for n = 0..10000</a>

%H Pontus von Brömssen, <a href="/A196251/a196251.png">Scatterplot of n, a(n) for n = 0..100000</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gilbreath%27s_conjecture">Gilbreath's_conjecture</a>

%H <a href="/index/Ge#Gilbreath">Index entries for sequences related to Gilbreath conjecture and transform</a>.

%t First /@ NestList[Abs[Differences[#]] &, PartitionsP /@ Range[0, 125], 125]

%Y Gilbreath transform of A000041.

%Y Cf. A036262, A362451.

%K nonn,look

%O 0,125

%A _Vladimir Reshetnikov_, Oct 27 2011