A080468 a(n) = A080578(n)-2n.

0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 3, 2, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 4

Offset: 2

Author

Benoit Cloitre, Oct 12 2003

Keywords

• nonn

Comments

Terms between 2^n and 2^(n+1) as n goes to infinity tend to the sequence : 0,1,2,1,2,3,2,1,2,3,2,3,4,3,2,1,2,3,2,3,4,3,2,3,4,3,4,5,4,3,2,1,....

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..16384

Crossrefs

Cf. A045412, A055938, A080578, A087805.

Programs

Mathematica

nn = 120; c[] := False; j = 1; c[1] = True; Reap[Do[Set[k, If[c[n], j + 1, j + 3]]; Set[{a[n], c[k], j}, {k - 2 n, True, k}]; Sow[a[n]], {n, 2, nn}] ][[-1, -1]] (* _Michael De Vlieger, Apr 29 2023 *)

Formula

a(2^n) = 0; Sum_{k=2^n..2^(n+1)} a(k) = n*2^(n-1) = A001787(n).