A072609 Changing of parity of remainder A072608(n) from alternation [..010101..] to steadily 1-range [...1111..]. AC-range corresponds to 0, while DC-range labeled by 1.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Formula

a(n)=Mod[A004648(n), 2]*Mod[A004648(n+1), 2]= A072608(n)*A072608(n+1)

Example

Take n = 11,12,13,14: A004648[n]=9,1,2,1. Parity A072608(n) = 1,1,0,1. So ..11.. transforms into 01 between n = 11 and n = 12: a(11) = 1, a(12)=0. With increasing n, A072609(n) changes from ..0000.. into ...1111. reflected by this sequence. by a range consisting only of 1-s. This secondary alternation also goes on.

Mathematica

mm[x_] := Mod[Mod[Prime[x], x], 2] Table[mm[w]*mm[w+1], {w, 1, 256}]
Times@@@Partition[Table[Mod[Mod[Prime[n], n], 2], {n, 110}], 2, 1] (* Harvey P. Dale, Dec 21 2014 *)

Crossrefs

Cf. A004648, A072608.

Sequence in context: A214210 A056029 A204547 * A185012 A328794 A185706

Adjacent sequences: A072606 A072607 A072608 * A072610 A072611 A072612

Keyword

nice,nonn

Author

Labos Elemer, Jun 24 2002

Status

approved