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.
25 (= 2^(2*2) + 2^(2*0) + 2^(1+2*1)) encodes the game {-1,0|1}, where, as the option -1 is dominated by option 0, the former can be deleted, giving us the game {0|1}, i.e. the canonical (minimal) form of the game 1/2, encoded as 2^(2*0) + 2^(1+2*1) = 9, thus a(25)=9 and a(9)=9. Similarly a(65536)=1, as 65536 (= 2^(2*(2^(1+2*1)))) encodes the game {{|1}|}, which is reversible to the game {0|}, i.e. the game 1, which is encoded as 2^(2*0) = 1.
Game {0|} is encoded as 2^(2*0) = 1, thus 1 is the first term of this sequence. Also 17 belongs into this sequence, as it encodes game {-1,0|}, where, as the option -1 is dominated by option 0, the former can be deleted, resulting the same game {0|}. Also code 65536 (= 2^(2*(2^(1+2*1)))) belongs into this sequence, as it encodes the game {{|1}|}, which is reversible to game 1.
Game {|0} is encoded as 2^(1+2*0) = 2, thus 2 is the first term of this sequence. Also 10 belongs belongs into this sequence, as it encodes game {|0,1}, where, as the option 0 dominates the option 1, the latter can be deleted, resulting the same game {|0}. Likewise code 8589934592 (= 2^(1+(2*2^(2*2)))) belongs into this sequence, as it encodes the game {|{-1|}}, which is reversible to game -1.
Game {1|} is encoded as 2^(2*1) = 4, thus 4 is the first term of this sequence. Also 5 belongs into this sequence, as it encodes game {0,1|}, where, because the option 1 dominates the option 0 on the left side, the zero can be deleted, resulting the same game {1|}.
Game {1|0} is encoded as 2^(2*1) + 2^(1+2*0) = 6, thus 6 is the first term of this sequence. Also 7 belongs into this sequence, as it encodes game {0,1|0}, where, as the option 1 dominates the option 0 on the left side, the former can be deleted, resulting the same game {1|0}.
Game {0|1} is encoded as 2^(2*0) + 2^(1+2*1) = 9, thus 9 is the first term of this sequence. Also 25 (= 2^(2*2) + 2^(2*0) + 2^(1+2*1)) belongs into this sequence, as it encodes game {-1,0|1}, where, as the option -1 is dominated by option 0, the former can be deleted, resulting the same game {0|1}.
Game {1|1} is encoded as 2^(2*1) + 2^(1+2*1) = 12, thus 12 is the first term of this sequence. Also 13 belongs into this sequence, as it encodes game {0,1|1}, where, as the option 0 is dominated by option 1, the former can be deleted, resulting the same game {1|1}.
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