A173524 - OEIS

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

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OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..100.

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]

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

CROSSREFS

Cf. A000120, A053737, A063787.

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

Sequence in context: A273149 A151925 A106653 * A049865 A070771 A274640

Adjacent sequences: A173521 A173522 A173523 * A173525 A173526 A173527

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 20 2010

STATUS

approved