Search: id:A048623
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%I A048623
%S A048623 2,3,4,5,9,6,10,17,8,33,18,65,12,129,34,257,16,66,20,130,513,1025,36,
%T A048623 258,2049,24,4097,68,8193,514,40,1026,16385,132,32769,2050,260,65537,
%U A048623 72,32,131073,4098,8194,136,262145,16386,524289,48,516,1048577,1028
%N A048623 Binary encoding of semiprimes (A001358).
%C A048623 Permutation of A048645 (without the term 1).
%e A048623 Squares p_i^2 are encoded with a single bit in position i (e.g. 25=ithprime(3)*ithprime(3) 
               => 2^3 = 8) and other terms p_i*p_j are encoded with two bits, as 
               sum 2^(i-1)+2^(j-1)
%p A048623 nthprime := proc(n) local i; if(isprime(n)) then for i from 1 to 1000000 
               do if(ithprime(i) = n) then RETURN(i); fi; od; else RETURN(0); fi; 
               end; # nthprime(2) = 1, nthprime(3) = 2, nthprime(5) = 3, etc.
%p A048623 bef := proc(n) local s,d; s := 0; for d in ifactors(n)[ 2 ] do s := s 
               + d[ 2 ]*(2^(nthprime(d[ 1 ])-1)); od; RETURN(s); end; # bef = Binary 
               Encode Factorization.
%p A048623 encode_semiprimes := proc(upto_n) local b,i; b := [ ]; for i from 1 to 
               upto_n do if((3 = tau(i)) or ((0 <> mobius(i)) and (4 = tau(i)))) 
               then b := [ op(b), bef(i) ]; fi; od: RETURN(b); end;
%Y A048623 Cf. A001358, A048639, A048672, A048645.
%Y A048623 Sequence in context: A096153 A083140 A124652 this_sequence A075161 A029636 
               A079871
%Y A048623 Adjacent sequences: A048620 A048621 A048622 this_sequence A048624 A048625 
               A048626
%K A048623 easy,nonn
%O A048623 1,1
%A A048623 Antti Karttunen, Jul 14 1999

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