A379728 - OEIS

%I #16 Jan 03 2025 15:49:54

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

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

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

%N Absolute value of first differences of paperfolding sequence A014577.

%H Paolo Xausa, <a href="/A379728/b379728.txt">Table of n, a(n) for n = 1..10000</a>

%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2501.00784">Cloitre's Self-Generating Sequence</a>, arXiv:2501.00784 [math.CO], 2025.

%F Generated by infinitely iterating the morphism a->ab, b->cd, c->ef, d->cd, e->ab, f->gh, g->ef, h->gh, starting with a, followed by mapping a,d,f,g to 0 and b,c,e,h to 1.

%t Abs[Differences[(1 + JacobiSymbol[-1, Range[100]])/2]] (* _Paolo Xausa_, Jan 03 2025 *)

%t Abs[Differences[Array[Boole[BitAnd[#, BitAnd[#, -#]*2] == 0] &, 100]]] (* _Paolo Xausa_, Jan 03 2025, after _Joerg Arndt_ C++ code in A014577 *)

%Y Cf. A014577, A343173 (signed version), A157196 (run lengths).

%K nonn

%O 1

%A _Jeffrey Shallit_, Dec 31 2024