Search: id:A050229
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%I A050229
%S A050229 1,2,3,5,11,13,19,29,37,53,59,61,67,83,101,107,131,139,149,163,173,179,
%T A050229 181,197,211,227,269,293,317,347,349,373,379,389,419,421,443,461,467,
%U A050229 491,509,523,541,547,557,563,587,613,619,653,659,661,677,701,709,757,773,
               787,797,821,827,829,853,859,877,883,907,941,947
%N A050229 Numbers n such that for any x, 1<=x<=n-1, there is y, 0<=y<=n-2, such 
               that x^2 ( mod n) = 2^y ( mod n).
%C A050229 It seems that sequence consists of {1,2} union A001122. The sequence 
               differs from A082595 because here the multiplicity is not important 
               (see example : P contains two 5's and Q is required to have at least 
               one 5, not necessarily 2 5's.)
%C A050229 Numbers n for which there is a permutation of 0..n-1 such that each number 
               is the sum of all the previous, plus 1, mod n. - Ron Hardin (rhhardin(AT)att.net), 
               Dec 28 2007
%e A050229 The set of values for x^2 mod 19, 1<=x<=18, is P=[1, 4, 9, 16, 6, 17, 
               11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1], the set of values for 2^y 
               mod 19, 0<=y<=n-2 is Q= [1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 
               11, 3, 6, 12, 5, 10] which contains all values in P, hence 19 is 
               in the sequence.
%o A050229 (PARI) for(n=1,450,if(sum(y=1,n-1,if(setsearch(Set(vector(n-1,x,2^(x-1)%n)),
               y),0,1))==0,print1(n,",")))
%Y A050229 Cf. A001122, A082595.
%Y A050229 Sequence in context: A153002 A042999 A089194 this_sequence A053184 A020607 
               A128425
%Y A050229 Adjacent sequences: A050226 A050227 A050228 this_sequence A050230 A050231 
               A050232
%K A050229 nonn
%O A050229 1,2
%A A050229 Benoit Cloitre (benoit7848c(AT)orange.fr), May 08 2003
%E A050229 More terms from Ron Hardin (rhhardin(AT)att.net), Dec 28 2007

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