A062173 a(n) = 2^(n-1) mod n.

0, 0, 1, 0, 1, 2, 1, 0, 4, 2, 1, 8, 1, 2, 4, 0, 1, 14, 1, 8, 4, 2, 1, 8, 16, 2, 13, 8, 1, 2, 1, 0, 4, 2, 9, 32, 1, 2, 4, 8, 1, 32, 1, 8, 31, 2, 1, 32, 15, 12, 4, 8, 1, 14, 49, 16, 4, 2, 1, 8, 1, 2, 4, 0, 16, 32, 1, 8, 4, 22, 1, 32, 1, 2, 34, 8, 9, 32, 1, 48, 40, 2, 1, 32, 16, 2, 4, 40, 1, 32, 64, 8, 4, 2, 54, 32, 1, 58, 58, 88, 1, 32, 1, 24, 46

Offset: 1

Author

Henry Bottomley, Jun 12 2001

Keywords

• nonn

Comments

If p is an odd prime then a(p)=1. However, a(n) is also 1 for pseudoprimes to base 2 such as 341.

Examples

			a(5) = 2^(5-1) mod 5 = 16 mod 5 = 1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..101101 (first 1000 terms from Harry J. Smith)
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A000079, A001567, A015910, A015919, A062172.

Cf. A082495, A106262, A257531, A305890.

Cf. A176997 (after the initial term, gives the positions of ones).

Programs

Haskell

import Math.NumberTheory.Moduli (powerMod)
a062173 n = powerMod 2 (n - 1) n  -- Reinhard Zumkeller, Oct 17 2015

Magma

[Modexp(2,n-1,n): n in [1..110]]; // G. C. Greubel, Jan 11 2023

Mathematica

Array[Mod[2^(# - 1), #] &, 105] (* Michael De Vlieger, Jul 01 2018 *)
Array[PowerMod[2,#-1,#]&,120] (* Harvey P. Dale, May 17 2023 *)

PARI

A062173(n) = if(1==n, 0, lift(Mod(2, n)^(n-1))); \\ Antti Karttunen, Jul 01 2018

SageMath

[power_mod(2,n-1,n) for n in range(1,110)] # G. C. Greubel, Jan 11 2023

Formula

a(n) = A106262(2*n-3, n-2). - G. C. Greubel, Jan 11 2023

Extensions

More terms from Antti Karttunen, Jul 01 2018