A064367 a(n) = 2^n mod prime(n), or 2^n = k*prime(n) + a(n) with integer k.

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

1,3

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

Formula

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

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 *)

Prog

(PARI) { p=1; for (n=1, 1000, write("b064367.txt", n, " ", (p*=2) % prime(n)) ) } \\ Harry J. Smith, Sep 12 2009

Crossrefs

Cf. A000040, A000079, A015910.

Sequence in context: A367300 A103245 A019242 * A113980 A095675 A340806

Adjacent sequences: A064364 A064365 A064366 * A064368 A064369 A064370

Keyword

nonn

Author

Labos Elemer, Sep 27 2001

Extensions

Definition corrected by Harry J. Smith, Sep 12 2009

Status

approved