A085765 Partial sums and bisection of A086450.

1, 2, 4, 5, 9, 11, 16, 17, 26, 30, 41, 43, 59, 64, 81, 82, 108, 117, 147, 151, 192, 203, 246, 248, 307, 323, 387, 392, 473, 490, 572, 573, 681, 707, 824, 833, 980, 1010, 1161, 1165, 1357, 1398, 1601, 1612, 1858, 1901, 2149, 2151, 2458, 2517

Offset: 0

Author

Ralf Stephan, Jul 22 2003

Keywords

• nonn
• easy

Comments

Sum of inverses of a(n) is 1.5398789314089581123...

Conjecture: log(a(n))/log(n) grows unboundedly.

Conjecture: a(n) mod 2 repeats the 7-pattern 0,0,1,1,1,0,1.

The conjecture concerning the mod 2 pattern follows directly from the corresponding conjecture proved in A086450. - Lambert Herrgesell (zero815(AT)googlemail.com), May 08 2007

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Programs

Maple

b:= proc(n) local m; b(n):= `if`(n=0, 1,
      `if`(irem(n, 2, 'm')=1, b(m), a(m)))
    end:
a:= proc(n) a(n):= b(n) +`if`(n=0, 0, a(n-1)) end:
seq(a(n), n=0..100);  # Alois P. Heinz, Sep 26 2013

Mathematica

b[0] = 1;
b[n_] := b[n] = If[EvenQ[n], Sum[b[n/2-k], {k, 0, n/2}], b[(n-1)/2]]; A085765 = Table[b[n], {n, 0, 100}] // Accumulate (* Jean-François Alcover, Mar 28 2017 *)

PARI

v=vector(1000);v[1]=1;s=1;for(n=2,1000,v[n]=if(n%2==0,v[n/2],s=s+v[(n+1)/2];print1(s",");s))

PARI

lista(nn) = {v=vector(nn); v[1]=1; s=1; for(n = 2, nn, v[n]= if(n%2==0, v[n/2], s=s+v[(n+1)/2])); forstep(i = 1, nn, 2, print1(v[i], ", "););} \\ Michel Marcus, Sep 26 2013

Formula

a(n) = A086450(2n) = A086450(0) + ... + A086450(n). - Charles R Greathouse IV, Sep 26 2013