

A173524


a(n) = A053737(4^k+n1) in the limit k>infinity, where k plays the role of a row index in A053737.


6



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+n1) where k>= ceil( 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+b1} 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/(b1); k := ceil(log(k)/log(b)) ; A053737(b^k+n1) ; end if; end proc:
seq(A173524(n), n=1..100) ; # R. J. Mathar, Dec 09 2010


CROSSREFS

Cf. A000120, A053737, A063787, A173523  A173536.
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



