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