A111397 Composite numbers (modulo 3).

1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 0, 1, 0, 2

Offset: 1

Author

Robert G. Wilson v, Nov 11 2005

Keywords

• nonn

Comments

If the terms of this sequence are interpreted as the base-3 expansion of a real number, its value is 0.4124999703972179190135867434954940067125524729635148630103267345... and its continued fraction expansion is 0, 2, 2, 2, 1, 4, 5278, 131, 4, 2, 2, 2, 2, 1, 24, 12, 1, 1, 7, 552, 1, 2, 1, ... with increasing partial quotients 2, 4, 5278, 66292, 274715, 420778, 625399, ...

Crossrefs

Cf. A002808, A073867.

Programs

Mathematica

Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; Table[ Mod[Composite[n], 3], {n, 105}]

Formula

a(n) == A002808(n) (mod 3).