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A173524 a(n) = A053737(4^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053737. 7
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A273149 A151925 A106653 * A049865 A070771 A274640
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 20 2010
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)