Mr.ǥ
󤬤Ϥäꤷ16ͤΥȡʥȹͤ
1̤ޤޤǡ16-115
1̤ΤΤ餱ͤǥȡʥȤ򤷤ƾ夬äΤ2
Ȥʤ
٤Ƥǡ15+318ʻˡʲˤȹͤޤ
109ڡ 0:13:05 42498
ǯ
ȡʥǰֽŤΤơ15ˡֽŤΤ餱4ġ3ˤܤ˽ŤΤ롣
񤭹顢Mr.ǥƱǤ
109ڡ 0:13:30 42499
٥륯åĥ
ȡʥȤǰ̤ᡢ̤βǽΤϰ̤ʤΤǤ4ĤǺ٥ȡʥȡȹͤޤ

׸3ʬ᤮ƤƹƤƥ٤ʤФ뤤ϡ
109ڡ 0:16:29 42500
ʪ
ȡʥɽͤޤ
ǽ







|||||||||||||||


ΥȡʥȤ15硣
ޤǿʤ1̤äʬƼΤ
2̤ˤʤ븢롣
4Ģ3
15+3=18

ܡ 109ڡ 0:25:28 42501
٥륯åĥ
ߤʤƱΤ褦Ǥ͡
ƱŤʬƼ˰Ĥ㤦ŤʤޤȤ̤Ǥ㤦ʣĤޤȤƤʤΤǡХХ̤뤷ʤʤȡ
109ڡ 0:21:10 42502

ߤʤƱǤ
촶(ۤȤʤ)ϡ11ʤ1̤15ǷޤΤǺ15󡢿ĤĤΤ뤳Ȥǽʤäȸ餻?äΤǤ

ˤϲ󤫤ΤǤ礦Σ
Τߤʤʬϡ(ͽ̤)狼2䤯餤8䤯餤ǤȤƤ⤪⤷äǤ

Ϻꡡ 109ڡ 1:14:52 42503
Mr.ǥ
#42503֣ˤϲ󤫤ΤǤ礦
71󤫤ʡ
2Ĥǡn(n+1)-1
(2+1)Ĥǡn^2+2n(ˡȤʤޤ

̸嵭͹ͤ˴㤤ꡢ嵭ͤϴְ㤤Ǥ뤳Ȥʬޤ
ߤʤ󡢥롼
109ڡ 9:28:36 42504
ϥ饮㡼ƥ
Ϥ褦ޤǧǤ
109ڡ 6:10:33 HomePage:湩ؤ˥42505
̤ꤹ
٤Ƥν뤳ȤϡǤʥȡ˵夷ޤ
N ĤǤ󤹤뤿Ӳ M ϡ ʲ­ɬפޤ

2^M >= N!

Ĥޤꡢ2 M ϡN γ礭ʤФޤɬ׾ˡ
ǡceil ڤ夲log2 2 ȤпɽؿȤȡ
M κǾ͡ʲ¡ˤϡʲμޤޤ

M = ceil(log2(N!))

ߤޤǤˡǧʾˤƤǾӲ K Ȥȡ
ʲɽΤ褦ˤʤäƤޤ

N: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
-------------------------------------------------------------------
M: 0 1 3 5 7 10 13 16 19 22 26 29 33 37 41 45 49 53 57 62 66 70
K: 0 1 3 5 7 10 13 16 19 22 26 30 34 38 42 46 50 54 58 62 66 71

ŤȻפޤN 12 19 22ǤϡK = M + 1 ˤʤäƤޤ

äȾܤΤꤿϡ󤪤ʤߤοŵOEISˤ
A036604 A001768 򸫤Ʋ
109ڡ 6:38:53 42506

#42504Mr.ǥ#42506̤ꤹꤵ
(ʬϹͤ褦ȤϤʤȤ)ʹ񿴤ˤ꤬Ȥޤ
ŵ¸ߤ⤳ǽΤäȤȤƤϡߤʤξQȤϤΥƤʬ¿Ȼפޤ(դʳΤߤʤ)ꤤޤ

109ڡ 8:27:04 42507
Mr.ǥ
#42504Ǥ
ĤΤν󤬷ޤäƤȤˡ+1ܤɤ뤫
ΤΡʶξ2ġˤӤƱ¦°Τξ
Τ飱ĤӤơ
ȹͤƤμǤ1ĤƤӤɬפϤʤ
Ʊ¦ΤΤΤʤȾȾ˻ĤȾȾȹͤС
Ӳäṳ̂Ǥ뤳Ȥʬޤ
ʤޤ
Ρ#42506ΡM = ceil(log2(N!))μˤʤΤˤϤˤ񤷤
109ڡ 10:49:20 42508
ޤ륱
GoogleäƤ͡
"A036604ɤ򸡺顢ȥåפ˿ŵOEISˤǤ衪

ǤäơOEIS"yoshikawa"򸡺ȡ

äƤ衪
ʤ硡 109ڡ 11:33:20 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42509

#42504Mr.ǥ#42506̤ꤹꤵ
(ʬϹͤ褦ȤϤʤȤ)ʹ񿴤ˤ꤬Ȥޤ
ŵ¸ߤ⤳ǽΤäȤȤƤϡߤʤξQȤϤΥƤʬ¿Ȼפޤ(դʳΤߤʤ)ꤤޤ

109ڡ 11:48:11 42510
uchinyan
Ϥˤϡơϡ
ࡤߤʤȤϤʤʡȤäȤäʤӤäꡤȤDz򤭤ޤ
⡤ǽϤɤͤ餤꤬꤬ԥʤäΤǤǤŤŤʤХʥꥵʡȵդ
θŪưפ˲򤱤ޤʴǡ

ܤ˽ŤŤ򸫤Ĥ櫓ǤΤˤϡޤȤʤǤŤŤ򸫤Ĥɬפޤ
ޤ16 ĤŬ 2 ĤĤ 8 ȤʬȤǽŤӤŤ 8 ĤӤޤˤ 8
ˡ 8 ĤŬ 2 ĤĤ 4 ȤʬȤǽŤӤŤ 4 ĤӤޤˤ 4
ˡ 4 ĤŬ 2 ĤĤ 2 ȤʬޡȤǽŤӤŤ 2 ĤӤޤˤ 2
ơ 2 ĤνŤӤŤ 1 ĤӤޤˤ 1
κǸ˻ĤäΤϡ˽ŤƱΤӤƤΤǡǽ 16 ĤǺǤŤŤǤ
ޤǤǡ8 + 4 + 2 + 1 = 15
Ťϣܤ˽ŤŤʤΤǡκǤŤŤӤƷڤä 4 ĤˤϤǤ
ΤʤС 4 İʳνŤϤ 4 ĤΤ줫ӤƤڤäǤ
ǡ 4 ĤǺǤŤŤ򸫤ĤС줬ܤ˽ŤŤˤʤޤ
Ʊͤˤơ2 + 1 = 3
ɡܤ˽ŤŤ򸫤Ĥˤϡ15 + 3 = 18 󡤤ɬפǤ

ȻפޤǾפʤΤʡ
¿ʬǽ˽񤤤褦ˡܤ˽ŤŤ򸫤ĤˤϴȤʤǤŤŤ򸫤ĤɬפȻפΤǡ
פȻפΤǤ
ͥνȡ 109ڡ 17:34:39 42511
Halt0
#42508 Mr.ǥ
1ӤˤĤ, ɤ餬ŤˤĤ2̤βǽΤ,
MӤȤ, ӷ̤ΥѥȤƹͤΤ2^M̤
, ʬƼνŤνȤƹͤΤN!̤
2^M̤η̤Ѥ, N!̤η̤ƶ̤뤿ˤ 2^M N ǤʤƤϤʤʤ. ä M ceil(log_2(N!)). ȤȻפޤ.

#42511 uchinyan
԰¤Ǥ, ̤ n ξ˺Ǿɾ n+ceil(log_2(n))-2 (ceil ڤ夲)Ǥ뤳ȤǤäݤǤ. ɤǤʤǤ
http://math.stackexchange.com/questions/1601/lower-bound-for-finding-second-largest-element
109ڡ 12:09:30 42512
uchinyan
ǼĤɤߤޤ

ϡƱͤǡ
ޤֽŤŤȡʥǷᡤ
˰ֽŤŤľܤӤƷڤäŤƱΤˤƥȡʥǰֽŤŤ롤
ȤͤΤ褦Ǥ͡
ǾΤʵϤʤǤ¿ʬ
ܤ˽ŤŤ򸫤ĤˤϴȤʤǤŤŤ򸫤Ĥɬפ롤
ȤȤפʤΤǤ礦

ʤ٤Ƥν֤Τǡ르ꥺǤͭ̾äǡץٶͤʤФ¸ΤǤ礦
ϡ#42506#42512ˤ褦ˡХʥ꥽ȤǤ
äȤ⡤򲿤ͽμʤϤǸĤΤϡʤѤȻפޤ

θ塤Ǿ˴ؤƤϡ#42512ΥǵƤ餷Ȥ𤬤ޤ
Halt0󡤾Ҳ򤢤꤬Ȥޤ
ͥνȡ 109ڡ 12:30:22 42513
baLLjugglermoka
ֽŤΤޤСܤƱ˷ޤȻפǤޤ
109ڡ 13:08:49 42514
baLLjugglermoka
Ʊ׻ޤ
http://www.nii.ac.jp/userdata/shimin/documents/H22/100714_2ndlec.pdf
109ڡ 13:16:27 42515
Mr.ǥ
#42512 Halt0ͭ񤦤ޤ
ʤۤɡȤ顡
2^M N Τ M ceil(log_2(N!)). M ceil(log_2(N!)). ȤʤΤǤ͡
ʡΤ褦ʤΤĤʤפФͤƤޤ
109ڡ 21:07:13 42516
ޤ
ȡʥDz򤭤ޤ
109ڡ 16:41:12 42517
⡼ޥ
16ǥͳ狼ޤ...
ޤĤĤʬơ줾ȤǰֽŤŤˤϡ󤺤Ĥ顢2*7=14󡣤ABȤơ٤Ȥ(15)BŤäȤȤ줬ֽŤ
ڤäνŤAȡŤäŤBȤΣܤ˽ŤäŤC٤(16)ACŤAܤ˽ŤCAŤCܤ˽ŤʬȻפΤǤ
ɤΤʤ ^^;...

̤PC饨ȥ꡼ƤޤOrz...
109ڡ 20:03:22 42518

⡼ޥ󤵤

Bޤޤ8ĤȤǡBľܽŤ٤ˡ
ACŤʬƼޤޤǽ뤫ǤϤʤǤ礦ġ(^_^;)?

󳧤Ʊˡ˹Ԥ夯ޤ
֤äƤޤޤ(^^;
Ǥ
109ڡ 20:51:19 42519
⡼ޥ
ʥޥޤ ^^
Ǥ ^^;
꤬Ȥޤ Orz
⤽CBȤ2ܤ˽ŤʤƤ狼ʤȤ˵դޤ...

4Ĥ4Ȥ顢3*4+3+3=18 λǤޤ
ڤǤ
109ڡ 21:29:13 42520
mukku
ʤۤɣܣߤƬʤ
109ڡ 22:24:31 42521
粬ҹ
פ֤ޤ̷Ǥ͡Ǥ˽񤫤Ƥ⤪뤫⤷ޤ󤬡ȡʥȤǤޤ

໲á̷ޤǡ

辡ˤϣࡡ̤ϷޤäƤΤǡĤꣳǣ̤ꡡ

äơܣᣱäݤǤʡäȻפäƤޤʡ
1011ڡ 10:41:52 42522
Ф
ޤȻפä̤ääʬƼ116ֹ򿶤
Ϥ˾褻Ȥ߹碌ʺ¦,¦ˤȽ񤯤Ȥˤ
1,2),,(1,16)216ΤֽŤW12W2Ф1W1W22Ĥľ褻٤롣

粬ҹ
ǼǤդޤǤæ˹
1012 7:53:05 MAIL:hbmath1965@yahoo.co.jp 42523
Mr.ǥ
#42522
ͥAȤȡ辡AȰ㤦֥å2Τ餱ϣ̤ˤʤ뤳ȤϤޤ
Τ褦A餱ब̤ˤʤ뤳ȤϤʤΤǡAä餱4
ΤʤǥȡʥȤ򤷤ƣ̤뤳ȤˤʤΤǤϤʤǤ礦
1012 13:38:58 42524
ޤ
ϡޤäΩͥåȤĴ٤ƤäȤorz
ϤϢˤϱ󤯵ڤӤޤġޡ

somewhere in the world 1012 18:13:06 42525
ʪ
70%ȡʥȤDz򤤤ƤǤ͡
ˡ֤ȤϻפޤޤǤ֤ȤϻפޤǤ
ܡ 1012 20:15:48 42526
⡼ޥ
#42524 Mr.ǥ
So do I ^^
ȡʥȯۤϽǤ͡
PC ^^
¨ ^^;v 1013ʷ 0:22:48 42527
ͺ
ޤ̤뤿˺ǤʿʥȡʥԤ15
ơΰ̰ʳˤ餱Ƥʤ4ĤǥȡʥԤ3
18
1013ʷ 18:09:27 42528
ͺ
ޤ̤뤿˺ǤʿʥȡʥԤ15
ơΰ̰ʳˤ餱Ƥʤ4ĤǥȡʥԤ3
18
1013ʷ 18:10:07 42529
٥륯åĥ
Фݤ
廮ŷŷФΰǤƱŤɤĴ٤뤳ȤϤǤƤ⡢ɤŤʬޤ󡣤ɤ餬ŤʬǤ
1014ʲС 1:50:41 42530

㲿󡢤ʤΤǡä㱿ɤϲǤǤ뤫äƤ꤫Ȼפä㤤ޤ
1014ʲС 21:39:25 42531
粬ҹ
#42524 Mr.ǥ
Ŧ꤬ȤޤŤ̡Ȥ



1 vs 2 3 vs 4 ˤʤǽ⤢Τǡ辡 1 vs 2ˤʤȤϸ¤ޤ󡣣̤Ƥ餳Σǣ̤ޤΤǡˤ꡼Ԥޤ

äơ̤Ƥ飳ɲäǡܣᣱƳޤ꤯ɤˤʤޤΤ褦ʹͤƤĺޤǼĺǤ礦

#42523 Ѥ
ƱդǤ

1014ʲС 23:13:43 42532
٥륯åĥ
粬ҹ
ȡʥȤ1̤ޤäʳǡ2̤βǽΤ4Ǥ
狼辡ޤǤΡͥȤʤä4Ϥ٤ơͥˤ餱ƤʤΤ2̤βǽޤ¾ΥͥʳĤޤ1̤Ǥʤ餱ƤޤΤǡ2̤βǽϤޤ
Ƥ4ǥȡʥȤԤȤ2̤ꤷޤ

ʤ2̤βǽब3ä硢򤹤ɬפϤʤ2ǽʬˤʤޤ

2̤ȸ2ܤ˶ȸäۤŬڤΤޤ͡
1015ʿ 0:13:03 42533
٥륯åĥ
äȾĹǤ͡ʬ䤹ä񤷤
1015ʿ 0:17:14 42534
Mr.ǥ
粬ҹ͡#42532ǽ񤫤Ƥ褦˹ͤƤΤǤȻפäƤϤޤ
٥륯åĥͤ#42533 դä
2ܤ˽ŤΤͥΤȣ䡢뤳Ȥ⤢Τǡ辡˻ĤäͥΰʳΡ
3ˣܤ˽ŤΤĤäƤȤݾڤϤʤȤΤθȤȤǤ
1015ʿ 0:42:33 42536