■剰余系と整数生成定規(その51)

  t={130,132,156,169,262,286,288,299,301,325,418,431,455,457,587}

に,底面積は半分の場合

  t={65.5,66,78,84.5,131,143,144,149.5,150.5,162.5,209,215.5,227.5,228.5,293.5}

も加えてみる.

  t={65.5,66,78,84.5,130,131,132,143,144,149.5,150.5,156,162.5,169,209,215.5,227.5,228.5,262,286,288.5,293.5,299,301,325,418,431,455,457,587}

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 差分集合

  d={65.5,0.5,12,6,5,45.5,1,1,11,1,5.5,1,5.5,6.5,6.5,40,6.5,11.5,1,33.5,24,2.5,5,5.5,2,24,93,13,24,2,130}

 整数と半整数に分けで整理してみたい.

  d={12,6,5,1,1,11,1,1,40,1,24,5,2,24,93,13,24,2,130}

={1,1,1,1,1,2,2,5,5,6,11,12,13,24,24,24,40,93,130}

  d={65.5,0.5,45.5,5.5,5.5,6.5,6.5,6.5,11.5,33.5,2.5,5.5}

={0.5,2.5,5.5,5.5,5.5,6.5,6.5,6.5,11.5,33.5,45.5,65.5}

 両方合わせると

  d={0.5,1,1,1,1,1,2,2,2.5,5,5,5.5,5.5,5.5,6,6.5,6.5,6.5,11,11.5,12,13,24,24,24,33.5,40,45.5,65.5,93,130}

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 まず,

  d={1,1,1,1,1,2,2,5,5,6,11,12,13,24,24,24,40,93,130}

で生成される整数を

  d={0.5,2.5,5.5,5.5,5.5,6.5,6.5,6.5,11.5,33.5,45.5,65.5}

で生成される整数で補っていくと,かなりの整数を生成することができる.

 これらでは無理であるが,もう少し生成子を加えていくと858まで可能であるという.

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