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A373212 Signature sequence of log(2).

%I A373212 #12 Jun 10 2024 00:13:48
%S A373212 1,1,2,1,2,3,1,2,3,1,4,2,3,1,4,2,5,3,1,4,2,5,3,1,6,4,2,5,3,1,6,4,2,7,
%T A373212 5,3,1,6,4,2,7,5,3,1,8,6,4,2,7,5,3,1,8,6,4,2,9,7,5,3,1,8,6,4,2,9,7,5,
%U A373212 3,10,1,8,6,4,2,9,7,5,3,10,1,8,6,4,11,2,9,7,5,3,10,1,8,6,4,11,2,9,7,5,12,3,10,1,8
%N A373212 Signature sequence of log(2).
%C A373212 Signature sequence of x = A002162: defined by sorting the values of i+j*x, i,j>=1, and collecting the list of the i in that order.
%C A373212 Starts similar to A023115, because log(2)=0.693147... is close to 1/sqrt(2) = 0.7071...
%H A373212 <a href="/index/Si#signature_sequences">Index entries for sequences related to signature sequences</a>
%p A373212 SIGSEQsort := proc(l1::list,l2::list)
%p A373212     if op(1,l1) < op(1,l2) then
%p A373212         return true ;
%p A373212     else
%p A373212         return false ;
%p A373212     end if
%p A373212 end proc:
%p A373212 SIGSEQ := proc(x,vmax)
%p A373212     local TBsrtd,i,j ;
%p A373212     TBsrtd := [] ;
%p A373212     for i from 1 do
%p A373212         if i > vmax then
%p A373212             break ;
%p A373212         end if;
%p A373212         for j from 1 do
%p A373212             if evalf(i+j*x) > vmax then
%p A373212                 break ;
%p A373212             end if;
%p A373212             TBsrtd := [op(TBsrtd),[evalf(i+j*x),i]] ;
%p A373212         end do:
%p A373212     end do:
%p A373212     sort(TBsrtd,SIGSEQsort) ;
%p A373212     [seq(op(2,v),v=%)] ;
%p A373212 end proc:
%p A373212 Digits := 100 ;
%p A373212 SIGSEQ(log(2),50.0) ;
%Y A373212 Cf. A002162.
%K A373212 nonn
%O A373212 1,3
%A A373212 _R. J. Mathar_, May 28 2024