A133436 - OEIS

%I #7 Mar 24 2016 11:18:11

%S 2,5,7,11,14,18,21,27,29,34,40,42,50,53,57,62,69,72,79,84,89,93,103,

%T 105,110,119,124,131,135,145,149,156,160,170,176,179,185,194,200,207,

%U 214,218,231,234,242,248,259,263,270,277,281,293,300,305,315,322,329,339

%N Generated by a kind of sieve (see Comments lines).

%C Start with the list of positive integers.

%C Call the current version of the list b(1), b(2), b(3), ...

%C Remove b(1) = 1 and renumber the terms.

%C Remove b(2) and b(2+1) from the remaining list and renumber the terms.

%C Remove b(3), b(3+2) and b(3+2+1) from the remaining list and renumber the terms.

%C Remove b(4), b(4+3), b(4+3+2) and b(4+3+2+1) from the remaining list and renumber the terms.

%C Repeat the process. What is left forms the sequence.

%H Austin C. Green and T. D. Noe, <a href="/A133436/b133436.txt">Table of n, a(n) for n=1..1000</a> (b-file extended and corrected).

%e a(3) = 7 because:

%e integer 1 is eliminated in the first round,

%e integers 3 and 4 are eliminated in the second round and

%e integers 6, 8 and 9 are eliminated in the third round.

%e This leaves the numbers 2, 5, 7...

%t lg = 1000; max = (lg+1)^2; Clear[p, bb, n]; p[1] = {{1}}; p[n_] := p[n] = Prepend[p[n-1]+n, {n}]; bb[n_] := bb[n] = Delete[bb[n-1], p[n]]; bb[0] = Range[max]; bb[n=1]; While[n <= lg && bb[n][[;; lg]] != bb[n-1][[;;lg]], n++]; A133436 = bb[n][[;;lg]] (* _Jean-François Alcover_, Mar 24 2016 *)

%K nonn,nice

%O 1,1

%A Austin C. Green (whyphi(AT)gmail.com), Nov 25 2007