A064367 a(n) = 2^n mod prime(n).

0, 1, 3, 2, 10, 12, 9, 9, 6, 9, 2, 26, 33, 1, 9, 28, 33, 27, 13, 48, 8, 36, 47, 4, 95, 20, 76, 62, 23, 4, 8, 117, 68, 25, 138, 64, 150, 43, 61, 10, 72, 156, 40, 12, 73, 51, 48, 41, 24, 26, 71, 48, 32, 16, 128, 173, 74, 110, 118, 59, 30, 247, 202, 208, 284, 53, 128, 32, 139

Offset: 1

Author

Labos Elemer, Sep 27 2001

Keywords

• nonn

Comments

Below the exponent n=10000, some integers (like 5,7,14,17,19,22,...,44, etc.) are not yet present among residues. Will they appear later?

For a(n) with n <= 10^6, the following residues have not yet appeared: {19, 22, 46, 52, 57, 65, 70, 77, 81, 85, 88, 90, 91, 103, 104, 106, 108, 115, 120, 122, 123, 125, ..., 15472319} (14537148 terms). - Michael De Vlieger, Jul 16 2017

Heuristically, the probability of 2^n mod prime(n) taking a given value is approximately 1/prime(n) for large n. Since the sum of 1/prime(n) diverges, we should expect each positive integer to appear infinitely many times in the sequence. However, since the sum diverges very slowly, the first n where it appears may be very large. - Robert Israel, Jul 17 2017

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000079, A015910.

Programs

Maple

seq(2 &^ n mod ithprime(n), n=1..100); # Robert Israel, Jul 17 2017

Mathematica

Array[PowerMod[2, #, Prime@ #] &, 69] (* Michael De Vlieger, Jul 16 2017 *)

PARI

a(n) = { lift(Mod(2,prime(n))^n) } \\ Harry J. Smith, Sep 12 2009

Formula

a(n) = A000079(n) mod A000040(n).

Extensions

Definition corrected by Harry J. Smith, Sep 12 2009