A292599 a(1) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)).

0, 1, 1, 2, 3, 2, 3, 4, 4, 6, 7, 4, 5, 6, 6, 8, 9, 8, 9, 12, 12, 14, 15, 8, 8, 10, 10, 12, 13, 12, 13, 16, 16, 18, 18, 16, 17, 18, 18, 24, 25, 24, 25, 28, 28, 30, 31, 16, 16, 16, 16, 20, 21, 20, 20, 24, 24, 26, 27, 24, 25, 26, 26, 32, 32, 32, 33, 36, 36, 36, 37, 32, 33, 34, 34, 36, 36, 36, 37, 48, 48, 50, 51, 48, 48, 50, 50, 56, 57, 56, 56, 60, 60, 62, 62, 32

Offset: 1

Author

Antti Karttunen, Sep 27 2017

Keywords

• nonn

Comments

1-bits in base-2 expansion of a(n) indicate the positions of primes in the sequence [n, floor(n/2), floor(n/4), ..., 1].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A010051, A078349, A292258, A292259, A292936.

Cf. also A292596 (variant for odd primes).

Programs

Maple

A292599 := proc(n)
    option remember;
    if n = 1 then
        0 ;
    else
        A010051(n) + 2*procname(floor(n/2)) ;
    end if;
end proc:
seq(A292599(n),n=1..100) ; # R. J. Mathar, Sep 28 2017

Mathematica

a[1] = 0; a[n_] := a[n] = Boole[PrimeQ[n]] + 2*a[Floor[n/2]]; Array[a, 96] (* Jean-François Alcover, Sep 29 2017 *)

Formula

a(1) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)).

Other identities. For all n >= 1:

A000120(a(n)) = A078349(n).

A007814(1+a(n)) = A292936(n).