A173524 a(n) = A053737(4^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053737.

1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9, 7, 8, 9, 10, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9, 4, 5, 6, 7

Offset: 1

Author

Omar E. Pol, Feb 20 2010

Keywords

• nonn

Comments

It appears that if A053737 is written as a triangle then the rows are initial segments of the present sequence; see the conjecture in A000120.

The comments in A173525 (base b=5 there) apply here with base b=4. The base b=3 is considered in A173523.

Crossrefs

Cf. A000120, A053737, A063787.

Cf. A173523, A173525, A173526, A173527, A173528, A173529.

Programs

Maple

A053737 := proc(n) add(d, d=convert(n,base,4)) ; end proc:
A173524 := proc(n) local b; b := 4 ; if n < b then n; else k := n/(b-1); k := ceil(log(k)/log(b)) ; A053737(b^k+n-1) ; end if; end proc:
seq(A173524(n),n=1..100) ; # R. J. Mathar, Dec 09 2010

Formula

a(n) = A053737(4^k+n-1) where k >= ceiling(log_4(n/3)). [R. J. Mathar, Dec 09 2010]

Conjecture: Fixed point of the morphism 1->{1,2,3,...,b}, 2->{2,3,4,...,b+1}, j->{j,j+1,...,j+b-1} for b=4. [Joerg Arndt, Dec 08 2010]