

A064367


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


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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: A214966 A103245 A019242 * A113980 A095675 A226442
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



