A379728 Absolute value of first differences of paperfolding sequence A014577.

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, 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, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0

Offset

1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Jeffrey Shallit, Cloitre's Self-Generating Sequence, arXiv:2501.00784 [math.CO], 2025.

Formula

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.

Mathematica

Abs[Differences[(1 + JacobiSymbol[-1, Range[100]])/2]] (* Paolo Xausa, Jan 03 2025 *)
Abs[Differences[Array[Boole[BitAnd[#, BitAnd[#, -#]*2] == 0] &, 100]]] (* Paolo Xausa, Jan 03 2025, after Joerg Arndt C++ code in A014577 *)

Crossrefs

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

Sequence in context: A100821 A139689 A204175 * A343173 A285255 A324823

Adjacent sequences: A379723 A379726 A379727 * A379729 A379732 A379737

Keyword

nonn,new

Author

Jeffrey Shallit, Dec 31 2024

Status

approved