A062174 -id:A062174 - cp's OEIS frontend

A062172 Table T(n,k) by antidiagonals of n^(k-1) mod k [n,k > 0].

0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 3, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 1, 0, 1, 0, 1, 0, 1, 4, 0, 0, 1, 0, 0, 1, 4, 3, 1, 5, 1, 3, 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 3, 7, 5, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 4, 7, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 5, 0, 7, 1, 3, 0, 3, 0, 1, 0

Offset: 1

Henry Bottomley, Jun 12 2001

			T(5,3)=5^(3-1) mod 3=25 mod 3=1. Rows start (0,1,1,1,1,...), (0,0,1,0,1,...), (0,1,0,3,1...), (0,0,1,0,1,...), (0,1,1,1,0,...), ...

Cf. A002997, A060154. Rows include A057427, A062173, A062174, A062175, A062176. Columns include A000004, A000035, A011655, A010684 with interleaved 0's, A011558, A010875. Diagonals include all the rows again and A000004 and A009001 unsigned.

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

Original entry on oeis.org

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

Mats Granvik, Mar 15 2010

Appears to be always either 0 or 1.

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

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

Cf. A174275, A062174.

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 *)

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

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

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

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A062172 Table T(n,k) by antidiagonals of n^(k-1) mod k [n,k > 0].

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

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