A072608 Parity of remainder Mod[p(n),n]=A004648(n).

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

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n)=Mod[Mod[p(n), n], 2]=Mod[A004648(n), 2]

Example

n=25:p(25)=97,Mod[97,25]=22, a(25)=Mod[22,2]=0. With increasing n, a(n) alternates:...010101..,followed after 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], {w, 1, 256}]
Table[Mod[Mod[Prime[n], n], 2], {n, 110}] (* Harvey P. Dale, Apr 22 2016 *)

Prog

(Haskell
a072608 n = a000040 n `mod` n `mod` 2 -- Reinhard Zumkeller, Dec 16 2013
(PARI) a(n)=prime(n)%n%2 \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A004648.

Sequence in context: A320007 A072165 A358224 * A295304 A171386 A189816

Adjacent sequences: A072605 A072606 A072607 * A072609 A072610 A072611

Keyword

nice,nonn

Author

Labos Elemer, Jun 24 2002

Status

approved