A373212 Signature sequence of log(2).

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, 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, 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

Offset: 1

Author

R. J. Mathar, May 28 2024

Keywords

• nonn

Comments

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.

Starts similar to A023115, because log(2)=0.693147... is close to 1/sqrt(2) = 0.7071...

Links

• Index entries for sequences related to signature sequences

Crossrefs

Cf. A002162.

Programs

Maple

SIGSEQsort := proc(l1::list,l2::list)
    if op(1,l1) < op(1,l2) then
        return true ;
    else
        return false ;
    end if
end proc:
SIGSEQ := proc(x,vmax)
    local TBsrtd,i,j ;
    TBsrtd := [] ;
    for i from 1 do
        if i > vmax then
            break ;
        end if;
        for j from 1 do
            if evalf(i+j*x) > vmax then
                break ;
            end if;
            TBsrtd := [op(TBsrtd),[evalf(i+j*x),i]] ;
        end do:
    end do:
    sort(TBsrtd,SIGSEQsort) ;
    [seq(op(2,v),v=%)] ;
end proc:
Digits := 100 ;
SIGSEQ(log(2),50.0) ;