🚀 go-pugleaf

$B1[6M!wBg:e650iBg$G$9!#(J
 
In article <1992Aug13.014435.16718@creo-rd.co.jp> suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:
>$BNkLZ!w%/%l%*#R!u#D$G$9!#(J
>$B#1=54VA0$K;d$,=P$7$?LdBj(J
>
>>$BLdBj(J
>>  $B2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $B$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
>>
>>    1  2  4  5  8  9  10  13  16  17  18  20  $B!&!&!&(J
>>    $B!JL58B$KB3$-$^$9!K(J
>
>$B$3$l$K$D$$$F!"$[$H$s$IH?1~$,$"$j$^$;$s$N$G!"%R%s%H$r=P$9$3$H$K$7$^$9!#(J

$B1[6M!wBg:e650iBg$G$9(J

$B$9$G$K$3$?$($,%]%9%H$5$l$?$H;W$C$F$^$7$?$,!"$-$N$;$$$+!)(J

$B4q?t$r$U$?$D$N$/$_$K$o$1$^$9!#(J
a: 1, 5, 9, 13, 17, 21   -----  4$B$G$o$C$F(J1$B$"$^$k!#(J
b:   3, 7, 11, 15, 19    -----  4$B$G$o$C$F(J3$B$"$^$k!#(J

A: 2$B$G3d$j@Z$l$k$@$13d$jB3$1$k$H(J a $B$N$I$l$+$K$J$k?t$N=8$^$j!#(J
B: 2$B$G3d$j@Z$l$k$@$13d$jB3$1$k$H(J b $B$N$I$l$+$K$J$k?t$N=8$^$j!#(J

$B$3$N(J A $B$r>.$5$$?t$+$i=g$KJB$Y$?$N$,$3$?$($G$O$J$$$G$7$g$&$+!)(J

A: 1,2,4,5,8,9,10,13,16,17,18,20,21,25,26,29,
B: 3,6,7,11,12,14,15,19,22,23,24,27,28,30,

$B$"$l!<!"(J20$B$N$D$.$,(J21$B$K$J$C$F$7$^$C$?!#$&$&!<$`!#(J

K. Koshigiri
koshi@cc.osaka-kyoiku.ac.jp

$@9b66!w(J$@El9)Bg$G$9!#(J

In article <1992Aug13.014435.16718@creo-rd.co.jp> suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:

   >$@LdBj(J
   >  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
   >
   >    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
   >    $@!JL58B$KB3$-$^$9!K(J

$@!VBh#19`$+$iBh(Jr$@9`$^$G$,(J a1,a2,...,ar $@$G$"$k?tNs!W$OL58B$K$"$j$^$9!#Nc(J
$@$($P!"(J

  $@0lHL9`(J an=\sum_{k=1}^{r}Sk,

                    ak(n-1)(n-2)$@!D(J(n-k+1)(n-k-1)$@!D(J(n-r+1)(n-r)  
         $@$?$@$7(J Sk=--------------------------------------------
                       (k-1)(k-2)$@!D!&(J1$@!&(J(-1)$@!D(J(k-r)

$@$J$I$G$9!#!J$3$l$rMxMQ$9$l$PBh(Jr+1$@9`(J$@$K9%$-$J?t$r$b$C$F$3$i$l$k!#!K(J

$@!V=c?h$K!W?t3X$NLdBj$H$$$&$3$H$G$9$,!"$b$7$=$&$J$i$P>r7o$r$D$1$?J}$,$h(J
$@$$$H;W$$$^$9!#(J
--
            $@El5~9)6HBg3XBg3X1!Am9gM}9)3X8&5f2J%7%9%F%`2J3X@l96(J
                        $@9b66(J $@??8c(J  

In article <1992Aug13.014435.16718@creo-rd.co.jp> suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:

|>$@LdBj(J
|>  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N(J$@?tNs$G$7$g$&!)(J
|>
|>    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
|>    $@!JL58B$KB3$-$^$9!K(J
|
|$@$3$l$K$D$$$F!"$[$H$s$IH?1~$,$"$j$^$;$s$N$G!"%R%s%H$r=P$9$3$H$K$7$^$9!#(J
|
|$@0J2<$K%R%s%H$,=q$$$F$"$j$^$9(J$@!#(J

|(2) $@?tNs$O!"A08e4X78$,$"$k$o$1$G$O$J$/!"$"$k=89g$r>:=g$KJB$Y$?$b$N$G$9!#(J
                                         ^^^^^^^^^^^^^^^^^^^^^^^^^^
$@$"$C(J!

{ a^2 + b^2 | a, b $@$O@0?t(J }

$@$G$7$g$&!%$U$U$U!%(J
$@%,(J$@%&%9$N@0?t$N%N%k%`$N=89g$G$9$M!%(J
$@%,%&%9$N@0?t$NC19`%$%G%"%k$N%N%k%`$N=89g$+$J!$(J0$@$,$J$$$+$i!%(J

# $@$*$\$s(J$@$/$i$$$O%]%9%H$7$J$$$G$*$3$&$H;W$C$?$N$K$#!%!%(J
_  __  __
 ][  ][  ]$@1J9>(J $@9'5,(J nagae@an.isl.titech.ac.jp
[__][__][_ $@El9)Bg(J $@A|>pJs9)3X8&5f;\@_(J $@0B5o1!8&(J

$@IY;38)N)Bg3X$N>>1J$G$9!#(J

suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:
>$@NkLZ!w%/%l%*#R!u#D$G$9!#(J
>$@#1=54VA0$K;d$,=P$7$?LdBj(J

>>  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
>>
>>    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J

$@%+%s%K%s%0$r$7$^$7$?!#(J
A Handbook of Integer Sequence (Academic Press) $@$K$h$l$P!"(J

1 2 4 5 8 19 10 13 16 17 18 20 

$@$O(J The sum of 2 squares $@$@$=$&$G$9!#(J
$@<!$N?t$O(J 25 $@$@$=$&$G!";29MJ88%$,#2$D$"$,$C$F$$$^$7$?!#(J

Euler $@$N(J "Opera Omnia" 1911  Vol 1 pp 417  $@5Z$S(J
Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen,
	Series A. Vol 53 pp 872

$@$G$9!#(J

$@!t2?$,=q$$$F$"$k$N$+C/$+D4$Y$F$/$l$k$H$&$l$7$$$J(J

$@$A$J$_$K!"$3$NK\$K(J 1 2 4 5 $@$G$O$8$^$k?tNs!JM-8B$N$b$N$r4^$`!K$O(J
14$@8D:\$C$F$$$^$7$?!#(J
-- 
		$@>>1J(J $@6Q!wAm9g8&5f=j(J.$@IY;38)N)Bg3X(J
		matznaga@pu-toyama.ac.jp

$@>>K\!w#J#RAm8&(J

In article <TSHINGO.92Aug13161339@sysipi.sys.titech.ac.jp> tshingo@sys.titech.ac.jp (Shingo Takahashi) writes:
>   >$@LdBj(J
>   >  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
>   >
>   >    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
>   >    $@!JL58B$KB3$-$^$9!K(J
>
>$@!VBh#19`$+$iBh(Jr$@9`$^$G$,(J a1,a2,...,ar $@$G$"$k?tNs!W$OL58B$K$"$j$^$9!#Nc(J
>$@$($P!"(J
$@!JCfN,!K(J
>$@!V=c?h$K!W?t3X$NLdBj$H$$$&$3$H$G$9$,!"$b$7$=$&$J$i$P>r7o$r$D$1$?J}$,$h(J
>$@$$$H;W$$$^$9!#(J

$@5.J}$N8@$$J,$O$b$C$H$b$G$9$,!"$=$l$G$OG$0U$NM-8B8D$NMWAG$r<($7$F(J
$@$=$N?tNs$r$"$i$o$9$3$H$,!"$G$-$J$/$J$C$F$7$^$$$^$9!#(J
$@!J$b$7!"@53N$K5-=R$9$k$H$9$l$P!"$=$N?tNs$r@8@.$9$k%"%k%4%j%:%`$r(J
$@5-=R$;$M$P$J$k$^$$!#!K(J
$@$3$3$O!V>o<1E*$K!W9M$($F$[$7$$$b$N$G$9!#(J

$@>>K\??8c!!E4F;Am9g5;=Q8&5f=j(J

$@6a(J$@F#!wIY;NDL8&$G$9!#(J

In article <448@keu02.rtri.or.jp>
r2230@L8221C.rtri.or.jp (Shingo Matsumoto) writes:

:>  $@$3$3$O!V>o<1E*$K!W9M$($F$[$7$$$b$N$G$9!#(J

$@7k9=A0$K$J$j$^$9$,!"(Jsci.math $@$G$bF1MM$K!"=i9`$$$/$D(J$@$+$rM?$($?$@$1$G$O(J
$@?tNs$,FCDj$G$-$J$$$H$$$&;XE&$,$"$C$F!"!V5,B'$N%9%^!<%H$5!W$H$$$&OC$K$J$C(J
$@$?3P$($,$"(J$@$j$^$9!#!J5-;v$rJ]B8$7$F$$$J$$$N$G!":FAw$O$G$-$^$;$s(J(_ _)$@!K(J

$@$^$"!"?tNs$NLdBj$r=P$9;~$K$O!"Jd4V$K$h$k(J$@$b$N$O9M$($J$$$H$7$F$$$$$s$8$c(J
$@$J$$$s$G$9$+!)(J:-)

$@!t(J  $@JV2N$J$i$LJVLd!'<!$N""$K$O!"$I$s$J?t$,F~$k$G$7$g(J$@$&!)(J
$@!t(J                  $@$^$?!"?tNs$N5,B'$O!)(J
$@!t(J  0, 1, 2, 4, 5, 8, $@""(J, 14, 17, 26, 40, 41, $@""(J, 44, 53, 80, $@""(J, 122, ...
-----
	$@6aF#!wIY;NDL8&(J

$@9b66!wEl9)Bg$G$9!#(J

$@;d$b$"$N<j$N!V%/%$(J$@%:!W$O$h$/$d$j$^$9!#9%$-$JJ}$G$9!#$?$@!">o!9;W$C$F$$(J
$@$?$N$O!"!VBh#19`$+$iBh(Jr$@9`$^$G$,(J a1,a2,...,ar $@$G$"(J$@$k?tNs!W$N0lHL9`$O0l(J
$@0U$K7hDj$G$-$J$$!"$H$$$&0UL#$G?t3XE*$K$O!J$D$^$j?t3X$NLdBj$H$7$F$O!K%J(J
$@%s%;%s%9$G(J$@$"$m$&!"$H$$$&$3$H$G$9!#(J

$@$b$C$H$b!"$"$N$h$&$J?t$NNs$r@8$_=P$9GX8e$K$"$k5,B'$rH/8+$9$k$H$$$&$3$H(J
$@$K4X(J$@$7$F$O?t3XE*$J0U5A$,$"$k>l9g$b$"$k$H;W$$$^$9!#(J

In article <448@keu02.rtri.or.jp> r2230@L8221C.rtri.or.jp (Shingo Matsumoto) writes:

   $@5.J}$N8@$$J,$O$b$C$H$b$G$9$,!"$=$l$G$OG$0U$NM-8B8D$NMWAG$r<($7$F(J
   $@$=$N?tNs$r$"$i$o$9$3$H$,!"$G$-$J$/$J$C$F$7$^$$$^$9!#(J
   $@!J$b$7!"@53N$K5-=R$9$k$H$9$l$P!"$=$N?tNs$r(J$@@8@.$9$k%"%k%4%j%:%`$r(J
   $@5-=R$;$M$P$J$k$^$$!#!K(J


$@8@$o$l$F$$$k$3$H$r>/$7DO$_$+$M$^$9$,!"0lHLE*$K$O?t(J$@Ns$O<+A3?t$+$i<B?t$X(J
$@$N4X?t$G$9$+$i!"?tNs$rDj5A$9$k$K$O$3$N4X?t$rDj5A$7$J$/$F$O$J$i$J$$$H;W(J
$@$$$^$9!#3N(J$@$+$KM-8B8D$N9`$r<($7$FFCDj$N?tNs$rI=$9$3$H$O!"?t3X=q$K$*$$$F(J
$@$h$/9T$J$o$l$^$9$,!"$3$l$OA08e$NJ8L.$+$i(J$@?tNs$NDj5A$,L@$i$+$J>l9g$KMQ$$(J
$@$i$l$k4JJXK!$@$H;d$OM}2r$7$F$$$^$9!#A4$/?7$7$$?tNs$N!VDj5A!W$r:G=i$N?t(J
$@9`$r<($9$@$1$G9T$J$&$3$H$O!">/$J$/$H$b;d$OIaDL$N?t3X=q$K$*$$$F$O8+$?$3(J
$@$H$,$"$j$^$;$s!#(J

$@!J0J>e>>K\$5(J$@$s$N%3%a%s%H$r!V?tNs$NDj5A!W$K4X$9$k$b$N$H$7$FM}2r$7$^$7$?!#!K(J

In article <448@keu02.rtri.or.jp> r2230@L8221C.rtri.or.jp (Shingo Matsumoto) writes:

   $@$3$3$O!V>o<1E*$K!W9M$($F$[$7$$$b$N$G$9!#(J

$@!V%/%$%:(J$@$N>o<1!W$H$7$F$O!"LdBj:n@.<T$N0U?^$9$k2sEz$r$9$k!"$H$$$&$3$H$G(J
$@$7$g$&$+!#$=$N0UL#$G$O!";d$N%3%a%s%H$O(J$@!V%/%$%:$N2sEz!W$H$7$F$OITE,@Z$@$C(J
$@$?$+$bCN$l$^$;$s!#(J

$@!V?t3X$N>o<1!W$H$7$F$O!"KAF,$K=R$Y$?$h$&$J$3$H(J$@$@$H;W$C$F$$$^$9!#(J

$@:G=i$NEj9F$G$O$3$N0c$$$r;XE&$7$?$D$b$j$@$C$?$N$G$9$,!"I=8=$,$h$/$J$+$C(J
$@$?$h$&$G$9(J$@!#(J
--
            $@El5~9)6HBg3XBg3X1!Am9gM}9)3X8&5f2J%7%9%F%`2J3X@l96(J
                        $@9b66(J $@??8c(J