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Start with the sequence of natural numbers S(0)={1,2,3,...} and define, for i>0, S(i)=D(i)S(i-1), where D(i)A denotes the operation of deleting the a(1+[i/2])th term of A={a(1),a(2),a(3),...}. E.g. D(3){1,2,4,6,9,10,...} means to delete the a(1+[3/2])th = 2nd term of {1,2,4,9,10,...}, giving {1,4,9,10,...}. The given sequence is the limit of S(i) as i->inf.
1

%I #10 Aug 30 2024 10:19:37

%S 2,3,6,7,8,11,14,17,18,19,22,23,24,27,28,29,32,35,38,39,40,43,46,49,

%T 50,51,54,57,60,61,62,65,66,67,70,71,72,75,78,81,82,83,86,87,88,91,92,

%U 93,96,99,102,103,104,107,108,109,112,113,114,117,120,123,124,125,128,131

%N Start with the sequence of natural numbers S(0)={1,2,3,...} and define, for i>0, S(i)=D(i)S(i-1), where D(i)A denotes the operation of deleting the a(1+[i/2])th term of A={a(1),a(2),a(3),...}. E.g. D(3){1,2,4,6,9,10,...} means to delete the a(1+[3/2])th = 2nd term of {1,2,4,9,10,...}, giving {1,4,9,10,...}. The given sequence is the limit of S(i) as i->inf.

%C It appears that the first difference sequence of {a(n)} is A080426.

%e D(1){1,2,3,4,5,6,...}={2,3,4,5,6,7,...} (delete first term),

%e D(2){2,3,4,5,6,7,...}={2,3,5,6,7,8,...} (delete 3rd term),

%e D(3){2,3,5,6,7,8,9,...}={2,3,6,7,8,9,...} (delete 3rd term),

%e D(4){2,3,6,7,8,9,10,...}={2,3,6,7,8,10,...} (delete 6th term),

%e ...

%e Limiting case: {a(n)}.

%Y Cf. A080426.

%K nonn

%O 1,1

%A _John W. Layman_, Oct 29 2004