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%I A173524 #21 Jul 02 2019 02:59:22
%S A173524 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,
%T A173524 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,
%U A173524 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
%N A173524 a(n) = A053737(4^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053737.
%C A173524 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.
%C A173524 The comments in A173525 (base b=5 there) apply here with base b=4. The base b=3 is considered in A173523.
%F A173524 a(n) = A053737(4^k+n-1) where k >= ceiling(log_4(n/3)). [_R. J. Mathar_, Dec 09 2010]
%F A173524 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]
%p A173524 A053737 := proc(n) add(d, d=convert(n,base,4)) ; end proc:
%p A173524 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:
%p A173524 seq(A173524(n),n=1..100) ; # _R. J. Mathar_, Dec 09 2010
%Y A173524 Cf. A000120, A053737, A063787.
%Y A173524 Cf. A173523, A173525, A173526, A173527, A173528, A173529.
%K A173524 nonn
%O A173524 1,2
%A A173524 _Omar E. Pol_, Feb 20 2010

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