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

1,3

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

Table of n, a(n) for n=1..105.

Index entries for sequences related to signature sequences

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) ;

Crossrefs

Cf. A002162.

Sequence in context: A098053 A272907 A128117 * A023115 A194436 A061336

Adjacent sequences: A373209 A373210 A373211 * A373213 A373214 A373215

Keyword

nonn

Author

R. J. Mathar, May 28 2024

Status

approved