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

1,6

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.

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

Formula

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

Example

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

Mathematica

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

Prog

(PARI) A062173(n) = if(1==n, 0, lift(Mod(2, n)^(n-1))); \\ Antti Karttunen, Jul 01 2018
(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
(SageMath) [power_mod(2, n-1, n) for n in range(1, 110)] # G. C. Greubel, Jan 11 2023

Crossrefs

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

Cf. A082495, A106262, A257531, A305890.

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

Sequence in context: A327805 A276689 A091453 * A004558 A129699 A002349

Adjacent sequences: A062170 A062171 A062172 * A062174 A062175 A062176

Keyword

nonn

Author

Henry Bottomley, Jun 12 2001

Extensions

More terms from Antti Karttunen, Jul 01 2018

Status

approved