%I A065912
%S A065912 55,84,86,205,222,235,206,305,325,489,556,494,830,928,964,972,1046,976,
%T A065912 721,940,1162,1132,1065,871,1469,1289,1328,1477,1594,1253,1760,1604,
%U A065912 1782,1877,1883,1442,2002,2114,2144,1709,2112,1909,2277,2343,2492,2735
%N A065912 Fourth solution mod p of x^4 = 2 for primes p such that more than two 
               solution exists.
%C A065912 Conjecture: no integer occurs more than three time in this sequence. 
               Confirmed for the first 1182 terms of A014754 (primes < 100000). 
               In this section, there are no integers which do occur thrice. Moreover, 
               no integer is first, second, third or fourth solution for more than 
               three primes. Confirmed for the first 2399 terms of A007522 and the 
               first 1182 terms of A014754 (primes < 100000).
%F A065912 a(n) = fourth solution mod p of x^4 = 2, where p is the n-th prime such 
               that x^4 = 2 has more than two solutions mod p, i.e. p is the n-th 
               term of A014754.
%e A065912 a(3) = 86, since 113 is the third term of A014754, 27, 47, 66 and 86 
               are the solutions mod 113 of x^4 = 2 and 86 is the fourth one.
%o A065912 (PARI): a065912(m) = local(s); forprime(p = 2,m,s = []; for(x = 0,p-1, 
               if(x^4%p == 2%p,s = concat(s,[x]))); if(matsize(s)[2]>3,print1(s[4],
               ","))) a065912(3000)
%Y A065912 Cf. A040098, A007522, A014754, A065909, A065910, A065911.
%Y A065912 Sequence in context: A119224 A135984 A140377 this_sequence A039533 A157484 
               A027865
%Y A065912 Adjacent sequences: A065909 A065910 A065911 this_sequence A065913 A065914 
               A065915
%K A065912 nonn
%O A065912 1,1
%A A065912 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 29 2001