This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275152 #22 Apr 03 2022 22:53:02
%S A275152 1,2,3,4,5,8,6,7,9,11,10,13,12,14,15,16,17,19,18,20,21,25,32,22,26,23,
%T A275152 29,24,27,33,34,37,36,40,28,30,31,35,38,41,42,45,49,48,39,43,50,57,44,
%U A275152 52,46,53,64,47,58,51,65,68,66,54,55,72,56,59,81,61,60
%N A275152 Sequence of distinct integers (considered as fixed disconnected 1-dimensional polyominoes and) chosen according to a greedy algorithm so as to tile a half line (see Comments for precise definition).
%C A275152 The indexes of the ones in the binary representation of a number give the positions of the squares in the corresponding polyomino. Thus:
%C A275152 - the number 1 = 2^0 corresponds to the monomino with a square at X=0,
%C A275152 - the number 2 = 2^1 corresponds to the monomino with a square at X=1,
%C A275152 - the number 13 = 2^0 + 2^2 + 2^3 corresponds to the (disconnected) tromino with squares at X=0, X=2 and X=3.
%C A275152 Shifting a polyomino dX squares to the right is equivalent to multiplying the corresponding number by 2^dX.
%C A275152 We use the following algorithm to generate this sequence:
%C A275152 - we start with a half (open) line of empty squares with coordinates X>=0,
%C A275152 - repeatedly, we choose the least number not yet used, such that the corresponding polyomino (possibly shifted to the right) (1) fills the current first empty square (2) and does not overlap one of the previously chosen polyominoes.
%C A275152 Occasionally, the partial tiling is perfect (i.e., all filled squares are contiguous); A275157 gives the corresponding indexes.
%H A275152 Rémy Sigrist, <a href="/A275152/b275152.txt">Table of n, a(n) for n = 1..10000</a>
%H A275152 Rémy Sigrist, <a href="/A275152/a275152.gp.txt">PARI program for A275152</a>
%e A275152 The following table depicts the first terms, alongside the corresponding polyominoes ("X" denotes a filled square, "_" denotes an empty square):
%e A275152 n a(n) a(n) in binary Corresponding shifted polyominoes
%e A275152 - ---- -------------- --------------------------------
%e A275152 1 1 1 X
%e A275152 2 2 10 _X
%e A275152 3 3 11 XX
%e A275152 4 4 100 __X
%e A275152 5 5 101 X_X
%e A275152 6 8 1000 ___X
%e A275152 7 6 110 _XX
%e A275152 8 7 111 XXX
%e A275152 9 9 1001 X__X
%e A275152 10 11 1011 XX_X
%e A275152 11 10 1010 _X_X
%e A275152 12 13 1101 X_XX
%e A275152 13 12 1100 __XX
%e A275152 14 14 1110 _XXX
%e A275152 15 15 1111 XXXX
%Y A275152 Cf. A235264, A275157.
%K A275152 nonn,base
%O A275152 1,2
%A A275152 _Rémy Sigrist_, Nov 13 2016