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
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) a(n) = { lift(Mod(2, prime(n))^n) } \\ Harry J. Smith, Sep 12 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 27 2001
EXTENSIONS
Definition corrected by Harry J. Smith, Sep 12 2009
STATUS
approved