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%I #28 Jul 17 2017 02:25:11
%S 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,
%T 62,23,4,8,117,68,25,138,64,150,43,61,10,72,156,40,12,73,51,48,41,24,
%U 26,71,48,32,16,128,173,74,110,118,59,30,247,202,208,284,53,128,32,139
%N a(n) = 2^n mod prime(n), or 2^n = k*prime(n) + a(n) with integer k.
%C 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?
%C 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
%C 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
%H Harry J. Smith, <a href="/A064367/b064367.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000079(n) mod A000040(n).
%p seq(2 &^ n mod ithprime(n), n=1..100); # _Robert Israel_, Jul 17 2017
%t Array[PowerMod[2, #, Prime@ #] &, 69] (* _Michael De Vlieger_, Jul 16 2017 *)
%o (PARI) { p=1; for (n=1, 1000, write("b064367.txt", n, " ", (p*=2) % prime(n)) ) } \\ _Harry J. Smith_, Sep 12 2009
%Y Cf. A000040, A000079, A015910.
%K nonn
%O 1,3
%A _Labos Elemer_, Sep 27 2001
%E Definition corrected by _Harry J. Smith_, Sep 12 2009
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