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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A328794 A181837 A185706

Adjacent sequences:  A072606 A072607 A072608 * A072610 A072611 A072612

KEYWORD

nice,nonn

AUTHOR

Labos Elemer, Jun 24 2002

STATUS

approved

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Last modified September 25 15:27 EDT 2021. Contains 347658 sequences. (Running on oeis4.)