A023115 -id:A023115 - cp's OEIS frontend

A022776 Place where n-th 1 occurs in A023115.

1, 2, 4, 7, 10, 14, 19, 24, 30, 37, 45, 53, 62, 72, 82, 93, 105, 118, 131, 145, 160, 175, 191, 208, 225, 243, 262, 282, 302, 323, 345, 367, 390, 414, 439, 464, 490, 517, 544, 572, 601, 630, 660, 691, 723, 755, 788, 822, 856, 891, 927, 964, 1001

Offset: 1

Clark Kimberling

nonn

Positions of the integers when the numbers a + b*sqrt(2) are arranged in increasing order. - Clark Kimberling, Mar 16 2015

It seems the name of this sequence could also be "Indices where records occur in A007336". - Ivan N. Ianakiev, Sep 09 2019

			The ordering of numbers a+b*r, where r = sqrt(2) as in Comments, begins with 0, 1, r, 2, 1+r, 2r, 3, 2+r, 1+2r, 4, ... in which the positions of integers are 1, 2, 4, 7, 10.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A023115, A049474.

t = Table[n + 1 + Sum[Floor[(n - k)/Sqrt[2]], {k, 0, n}], {n, 0, 200}] (* A022776 *)
Differences[t] (* A049474 *) (* Clark Kimberling, Mar 14 2015 *)

a(n)=1+sum(k=1,n-1,ceil(k/sqrt(2))) \\ Benoit Cloitre, Jan 24 2009

a(n) = 1 + Sum_{k=1..n-1} ceiling(r*k) where r=1/sqrt(2). - Benoit Cloitre, Jan 24 2009

A373212 Signature sequence of log(2).

Original entry on oeis.org

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

R. J. Mathar, May 28 2024

nonn

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...

Index entries for sequences related to signature sequences

Cf. A002162.

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) ;

cp's OEIS Frontend

A022776 Place where n-th 1 occurs in A023115.

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