A174282 a(n) = 3^n mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.

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

Offset: 1

Author

Mats Granvik, Mar 15 2010

Keywords

• nonn
• easy

Comments

Appears to be always either 0 or 1.

This follows from Fermat's Little Theorem. - Charles R Greathouse IV, Feb 13 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A174275, A062174.

Programs

Mathematica

f[n_] := PowerMod[3, n - 1, Exp@ MangoldtLambda@ n]; Array[f, 105] (* Robert G. Wilson v, Jan 22 2015 *)
Table[Mod[3^(n-1) , E^(MangoldtLambda[n]) ], {n, 1, 100}] (* G. C. Greubel, Nov 25 2015 *)

PARI

vector(95,n,ispower(k=n,,&k);isprime(k)&k!=3) \\ Charles R Greathouse IV, Feb 13 2011

Formula

a(n) = A000244(n) mod A014963(n).

a(n) = 1 if n = p^k for k > 0 and p a prime not equal to 3, a(n) = 0 otherwise. - Charles R Greathouse IV, Feb 13 2011

Extensions

More terms from Robert G. Wilson v, Jan 22 2015