%I A059873
%S A059873 1,3,5,13,21,46,78,175,303,639,1143,2539,4542,9214,17406,36735,69374,
%T A059873 139254,270327,556031,1079294,2162678,4259819,8642558,17022974,34078590,
%U A059873 67632893,136249338,270401534,541064701,1077935867,2162163707
%N A059873 The lexicographically first sequence of binary encodings of solutions 
               satisfying the equation given in A059871.
%C A059873 The encoding is explained in A059872. Apply bin_prime_sum (see A059876) 
               to this sequence and you get A000040, the prime numbers.
%p A059873 primesums_primes_search(16); primesums_primes_search := (upto_n) -> primesums_primes_search_aux([],
               1,upto_n); primesums_primes_search_aux := proc(a,n,upto_n) local 
               i,p,t; if(n > upto_n) then RETURN(a); fi; p := ithprime(n); for i 
               from (2^(n-1)) to ((2^n)-1) do t := bin_prime_sum(i); if(t = p) then 
               print([op(a),i]); RETURN(primesums_primes_search_aux([op(a),i],n+1,
               upto_n)); fi; od; RETURN([op(a),`and no more found`]); end;
%Y A059873 Cf. A059459, A059874, A059875.
%Y A059873 Sequence in context: A106916 A034484 A059872 this_sequence A059874 A059875 
               A086893
%Y A059873 Adjacent sequences: A059870 A059871 A059872 this_sequence A059874 A059875 
               A059876
%K A059873 nonn
%O A059873 1,2
%A A059873 Antti Karttunen Feb 05 2001
%E A059873 More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Sep 12 
               2001
%E A059873 More terms from Larry Reeves (larryr(AT)acm.org), Nov 20 2003