

A026363


a(n) is the least k such that s(k) = n, where s = A026362.


7



1, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 38, 39, 41, 42, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 79, 80, 82, 83, 85, 86
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OFFSET

1,2


COMMENTS

Or, starting from the natural number, delete successively from the working sequence the term in position 2*a(n). From natural numbers, delete the term in position 2*1, i.e., 2. This leaves 1,3,4,5,6,7,8,9,10,11,... . Delete now the term in position 2*3=6, i.e., 7. This leaves 1,3,4,5,6,8,9,10,11,... . Delete now the term in position 2*4=8, i.e., 10. This leaves 1,3,4,5,6,8,9,11,... and so on.  Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 20 2007
The term deleted from the nth working sequence is equal to A026364(n), which means that all integers which are not in the present sequence are in A026364 and no others.  Philippe Lallouet (philip.lallouet(AT)orange.fr), May 05 2008
Complement of A026364; also the rank transform (as at A187224) of (A004526 after removal of its first three terms, leaving (1,2,2,3,3,4,4,5,5,6,6,...).  Clark Kimberling, Mar 10 2011
Positions of 1 in the fixed point of the morphism 0>11, 1>101; see A285430.
Conjecture: 1 < n*r  a(n) < 2 for n>=1, where r = (1 + sqrt(3))/2.  Clark Kimberling, Apr 29 2017


LINKS



FORMULA

a(1)=1, then a(n)=a(n1)+2 if n is even and n/2 is not in the sequence, a(n)=a(n1)+1 otherwise (in particular a(2k+1)=a(2k)+1). a(n)=(1+sqrt(3))/2*n+O(1). Taking a(0)=0, for n>=1 a(2n)a(2n2)=A080428(n).  Benoit Cloitre, Apr 23 2008


MATHEMATICA

seqA = Table[Floor[(n+2)/2], {n, 1, 180}] (* A004526 *)
seqB = Table[n, {n, 1, 80}]; (* A000027 *)
jointRank[{seqA_, seqB_}] := {Flatten@Position[#1, {_, 1}],
Flatten@Position[#1, {_, 2}]} &[Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@ seqB}, 1]];
limseqU = FixedPoint[jointRank[{seqA, #1[[1]]}] &, jointRank[{seqA, seqB}]][[1]] (* A026363 *)
Complement[Range[Length[seqA]], limseqU] (* A026364 *)
s = Nest[Flatten[# /. {0 > {1, 1}, 1 > {1, 0, 1}}] &, {0}, 13] (* A285430 *)
Flatten[Position[s, 0]] (* A026364 *)
Flatten[Position[s, 1]] (* A026363 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



