triacontahedron lover
9ΤȤ27ΤȤ81ΤȤǹͤƤäȳοƤޤ

ޥܽ񤤤0,1,2,3,4,9,10,12,13,...Ƚ˴ݤĤƤȤ褦䤯§Ƥޤ
102ڡ 0:25:28 42451

ȡ뽸ݤäǤ
102ڡ 0:26:39 42452
triacontahedron lover
ʬǽ񤤤Ƥʤ2ƤȤϲ
ȡ뽸ˤĤĴ٤ƤޤΤˤäݤäǤ
102ڡ 0:29:21 42453
CRYING DOLPHIN
ľǡ3ˡ2Ȥʤ󤹤ФΤʡȻפäɡǤʤ褦ǡġ
㤨С08ΤȤϡ0,1,3,4װʳˤ0,1,3,8פʤ⤢äꡣ
ȤȤǡطʤޤä狼̤ޤޤǤ
ï⤤ʤԳϡ 102ڡ 0:31:56 HomePage:֥⤢42454
triacontahedron lover
Ϣꤴʤ
ȡ뽸ߤ˹ͤʤ9ΤȤ81ΤȤ729ΤȤƤΤ餷Ǥ



















ʴǤ͡äƤǤ礦
102ڡ 0:34:29 42455

10^5ʲ顢ξ1991Ĥο٤뤳Ȥ򼨤
ɤλĤǤʤʤ

äƿ꤫ɤä꤬äȤפФޤ
102ڡ 0:34:39 42456

ΤĤ1983ǯIMO5֤Ǥ
ʸοͤ1991ʤ1983ߤǤ(ʤȤ2048ʲʤ餤)
102ڡ 0:48:02 42457

3ʿ1Ȥʤ
0,2,6,8,18,20,24,26,ġ
ȤΤͤƤޤʥȡ뽸
triacontahedron loverεˡڤ



Ǥ
No.424553ʿ2ȤʤѥǤ͡
102ڡ 0:48:51 42458
Mr.ǥ
7293^6()ȤȤǡ3ˡ˴طΤǤϤȹͤ
0,1,3,4,9,10,12,13,27ޤǵƤƤ顢3ʿľ
0,1Ф꤫ʤΤ
3ʿǡ1000000ʲΡ0,1Ф꤫ʤΡ2^6=64ʸġˤȤޤ

3ʿ1,0Ф꤫ʤۤʤ룲äơɤΰ̤20ˤʤ뤳Ȥ
ʤΤǡʿѤη¸ߤ뤳ȤϤʤפȤͳǤ褤Τʡ

0(3^n1)ޤǤϰϤǤϡ^n(ġ
񤷤ơϢ³ڤԥǤ
102ڡ 1:44:06 42459

Ф

CRYING DOLPHINˤȤƤᤤͤǤ
3ˡ01Τߤɽ0728ޤǤοޤ
Ͼ꤯Ǥޤ(^^;
3^kǤ2^kǤ褤Τ
ޤ褯狼äƤޤ(^^;

102ڡ 1:00:09 42461
٥륯åĥ
729ޤǤ65ǤʤʤΤȻפäƤ顢褯728ޤǤʤΤ64Ǥ
줿Τǹͤθڤϡơ
102ڡ 1:03:13 42462
٥륯åĥ
ʤߤˡδֳ֤ͤƻˡ§򸫤ĤƤߤޤ
1215121141215
102ڡ 1:05:11 42463
ϥ饮㡼ƥ
Ϥ褦ޤǧǤ
102ڡ 6:33:30 HomePage:湩ؤ˥42464
ޤ륱
Ʊ褦ˡ餿ᤷˡ§򸫤Ĥ˳ĥƣˤɤ夭ޤ

ǧΤᡢץ񤭡ȤȤǤʤΤ򸫤ĤƤޤޤ

Ĵ١ɷˤȿȤʿѤˤʤɷˤʤϤο򥫡ɷ˲äޤ
ñˣĴ٤ȡ
[0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 120, 121, 243, 244, 246, 247, 252, 253, 255, 256, 270, 271, 273, 274, 279, 280, 282, 283, 324, 325, 327, 328, 333, 334, 336, 337, 351, 352, 354, 355, 360, 361, 363, 364]
ΣΥɷǤޤ

ǤΤȤ120򥹥åפƤߤȤ
[0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 121, 201, 228, 237, 240, 244, 245, 247, 256, 258, 259, 261, 270, 280, 283, 292, 297, 298, 306, 327, 330, 331, 334, 343, 346, 360, 496, 497, 525, 534, 588, 589, 597, 613, 616, 666, 670, 671, 675, 678, 687, 705, 706, 713, 715, 718, 728]
ȡΥɷǤƤޤޤ

ȤȤǡϺ¿ǤϤʤ

㡢¿Ϥġ
ʤ硡 102ڡ 12:40:04 HomePage:ޤ륱42465
桼ȥ˥
̩Υڡޤ
Τ褦ʥΤäΤǤ͡
102ڡ 11:52:48 42466
桼ȥ˥
̩Υڡޤ
Τ褦ʥΤäΤǤ͡
102ڡ 11:58:49 42467
ޥ
褫Ǥ

¤ϤꡢˤĤƤϾǤ3ˡѤ64Ĥξ˺뤳ȤΤߤλ׹ͤǡ֤줬פȽꤷƤޤޤߤޤġ

ͥϡΤλͽǡ3ˡˤˡ⤽ˤޤ(ˤϸڤƤޤ)

бˤĤƤϡ()˹ͤޤǤ򤪤ޤ
102ڡ 13:02:53 42468

񤷤ä(Ȳ򤱤ƤʤΤǡ񤷤פ)Ǥ
äȤϲǤҥȤˤ뤾ȤȤ
ᣳѤ롩
(񤷤ΤǺ¤ΥҥȤͿƤȤ)ޥ뤵㡢ݥĥ뢪˴ؤꡩȤȤ
ĤĤ˿ڤä¤٤ȺǽΣĤ9ĤΣĤǡȥ롼פΤǽʿƤˡ§ϤʤĴ٤Ƥߤޤ
(餬ʤ狼ޤ)ǽΣĤΡߡߡߡߡߤΥѥ󤬡ĤҤȥ롼פˤȤɲäǤʤߤΥѥˤƧƤ롣ϤäȤΣĤҤȥ롼פ򣹸ĤޤȤ᤿ΤˤƧƤȤȤǾ˹礦ϡǽΣĤ4ĤϣˡĤ򣱸ĤȤ롼ףĤˣĤϣˡ롼ףĤ򣱸ĤȤ祰롼פĤˣģϣˡȤȤǣߣߣ᣶Ȥʤޤ
줿Τ϶Ǥ롩ߤʤΤߤơٶޤ
ʤˤƤ⺣󡢺ǯϢ³ȤδǥۥäȤޤ
102ڡ 13:31:31 42469

#42465ޥ뤱󤵤#42468ޥ뤵ε򸫤ʤǡ񤭹ߤ򤷤Ƥޤޤ
ޥ뤵󡢥ѥ֥դθѥΩĿȤȤƤФƲꡢհʳθդϤޤ󡣺⤭äȤߤʤ󤬤ƤƲΤǡȡ뽸硩졩(˵ѤǤޤ)ڤޤƤޤ
102ڡ 13:48:12 42470
ޤ륱
餯Ǥ飷Ǥʤ飳ˤУǤ褫äʡȻפäƤޤ
ȸȾȤʤǤ͡ʤΤǡäȤ餷ꤹȡ⤦ɤǤ礦͡

ʸߡץ󤷤ơȤ߹碌ȯޤ뤫ʡ
ʤ硡 102ڡ 13:58:02 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42471
uchinyan
Ϥˤϡơϡ
ࡤ褯ʬ餺ϤޤäƤޤޤ
729 = 3^6 ʤΤDzꤽʡȻפäΤΡޤ϶ŪĴ٤Ƥߤ뤫ȻפäΤѤäƤ褯ʤä⡣
礫ɤ褯ʬʤˡȤ⡤׹ͤή졤ȤǤʴ

ޤǽ餫餤øǤ0 ꤽʡȤ櫓ǡ0 Ϥơ0, 1, 3 3 ġޤ
ǡֺǸ 3 򤹤٤Ƥ­Ρ3, 4, 6Ϥδ֤ǤϾʤΤǡ
ȡ0, 1, 3Ȥδ֤Ǿ褦ˤФ褯ϡ0, 1, 3, 4 4 ġ
ˡƱͤˤ٤Ƥ 4 ­ȡ4, 5, 7, 8Ǥȡ0, 1, 3, 4Ϥޤޤ
ʤΤǡ8 + 1 = 9 ɲä0, 1, 3, 4, 9 5 ġͤȤޤޤ줬Ǥ͡
ǡ0, 1, 3, 4, 9˰ֺǸ 9 򤹤٤Ƥ­Ρ9, 10, 12, 13, 18ͤ
ȡ0, 1, 3, 4, 9Ȥδ֤Ǿ褦ˤФ褯ϡ0, 1, 3, 4, 9, 10, 12, 13 8 ġ
Ϥ٤Ƥ 13 ­ޤϤäƤߤȤޤ13 + 13 = 26 μ 27 ɲäơ
0, 1, 3, 4, 9, 10, 12, 13, 27 9 ġޤ
ޤǤе§⸫ƤޤǰΤˤ⤦ȡ
0, 1, 3, 4, 9, 10, 12, 13, 27 27, 28, 30, 31, 36, 37, 39, 40, 54 ǡ
0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40 16 ġ
Τ٤Ƥ 40 ­ΤȤȤϤޤ40 + 40 = 80 μ 81 ɲäơ
0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 81 17 ġ
ɡ
0 (3^n - 1)/2 2^n ġ0 3^n - 1 2^n ġ0 3^n 3^n ǽ 2^n + 1 ġ
ϰϿŪǼˡǤǤǤ礦
ޤǤ⡤ɷ 0 ޤʤСǤ
嵭ιˡ餫ȤȡäȼϤޤ

Ǥϡ0 728 = 729 - 1 = 3^6 - 1 ΥɤʤΤ 2^6 = 64 硤ˤʤޤ

ޤǹͤơɤ 3 ˡǤʡȵդޤ
ȤʤΤʤʤȤ嵭ιͤطʤˤϤʤ뤫ʡ

̤ˡ 3 ˡɽ 0, 1, 2 ɽޤ
0 3^n - 1 Ǥ 012 θ
㤨 0 1 ɽۤʤΣĤ¤ 0 2 ˤʤ뤳ȤϤʤ
äƤ 2 dzäʿѤ0 1 ɽʤȻפޤ
ǡ¿ʬ¿ʬϤʤŤ¿ʬ0 1 ǤǤ򽸤դΤǤ礦
줬С0 3^n - 1 0 1 ɽθĿ 2^n ĤʤΤǡ
դɷ 2^n ˤʤޤ

ϡǼĤɤٶޤ
ͥνȡ 103ʶ 18:00:24 42472

ޤ륱󤵤˿ȯơ0,728,1,727,2,726,ġĤȤǥåƤץ
0 1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 81 82 84 85 90 91 93 94 108 109 111 112 117 118 120 121 243 244 246 247 252 253 255 256 270 271 273 274 279 280 282 283 607 608 610 611 616 617 619 620 634 635 637 638 643 644 646 647 688 689 691 692 697 698 700 701 715 716 718 719 724 725 727 728
Ȥ80ĤȤ߹碌ϸĤޤ

3ʿɽ
0[01][01][01][01][01] 32
10[01][01][01][01] 16
2[12][12][12][12][12] 32
η80Ĥˤʤޤ
Ϥޤ狼ޤ󡣤äȾʤʬϤȲǤġ
102ڡ 14:27:01 42473
⡼ޥ
äȤ^^; (ޤOrz)
729=3^6
äϡ728ޤǤʤΤǡ
ŷǹͤ...
0,3^0,3^1,3^2,3^3,3^4,3^5 ʬƼȤ߹碌ʤ=ʿͤϤʤ...
0­ƤѤʤΤǡ3^03^5ޤǤ6ĤʬƼʣĤ¤롣6C1+6C2+6C3+6C4+6C5+6C6=2^6-1
ˡ0ä뤳ȤǤΤǡ2^6=64

#42465 ߤȤʤ!!! 64礸ʤǤͤ ^^;
¨ ^^;v 102ڡ 15:03:18 42474
triacontahedron lover
ƤߤƺƸڡ̤äƤΤоηǤ

3ΤȤ
0,20,1(1,2)Ǻ2硣

9ΤȤ
0,2,6,80,2,3,5(3,5,6,8)0,1,3,4(4,5,7,8)1,2,4,5(3,4,6,7)0,2,5,7(1,3,6,8)
4Ȼפ䡣

0,1,3,7,8

(0,1,5,7,8)

5礬ȵդƤޤޤäȹͤƤޤ

Τ˸Ⱦ򤦤ޤȤäƤɤˤʤꤽǤͤƤޤ
102ڡ 14:48:36 42476
uchinyan
ǼĤɤߤޤ
ࡤϤ꤫ʤΤ褦Ǥ͡

ǥȤƤϡȡ뽸硤3 ˡʤɤ褦Ǥ
εϤʤץͤǡ
ϡ64 ǤϤʤΤȤϡ#42481 82 硤͡

Ȥǡȡ뽸äƲ ٶޤ (^^;
ͥνȡ 103ʶ 13:35:47 42477
٥륯åĥ
δֳ֤оФƤ뤳Ȥ顢64ǽΤ65ˤϤ1­ʤȤޤǤϳǧǤޤˤĤƤϸڤǤƤޤ
ץˤʳDzˡϤΤǤ礦
102ڡ 15:54:24 42478
triacontahedron lover
¸档
9λ4ѥ0,4,5,7(1,3,4,8)⤢ä

27λκ12äݤΤǤ9λ5Ĥäȹͤ13ˤʤȤ߹碌⤢ꤽ
Ȥꤢ9λ4ѥȺѥȤ߹碌12ʾˤȤ߹碌ͤ뤳Ȥˤ롣

ŪˤޤǤϺоΤǿؤǤޤ路ƤȤ褦ʵ롣ȤƤޤ
102ڡ 15:57:34 42479
ޤ륱
#42479
ȤȤϡ飲Ǥ͡
٤ȡĴ٤Ƥ⣶ä餤ФޤʴĶˤޤ
ʲ磱Σѥ

[0, 1, 5, 6, 8, 14, 18, 19, 21, 25, 26]
[0, 1, 5, 7, 8, 12, 18, 20, 21, 25, 26]
[0, 1, 5, 7, 11, 16, 18, 19, 23, 24, 26]
[0, 2, 3, 7, 8, 10, 15, 19, 21, 25, 26]
[0, 2, 3, 5, 11, 15, 16, 18, 23, 24, 26]
[0, 2, 3, 8, 10, 11, 15, 21, 23, 24, 26]
[0, 2, 3, 7, 8, 10, 15, 19, 21, 24, 26]
[0, 2, 5, 7, 11, 16, 18, 19, 23, 24, 26]
[0, 1, 4, 6, 10, 15, 17, 18, 22, 23, 25]
[0, 2, 3, 7, 8, 10, 15, 19, 21, 24, 25]
[1, 3, 4, 8, 9, 11, 16, 20, 22, 25, 26]
[1, 2, 5, 7, 11, 16, 18, 19, 23, 24, 26]
ʤ硡 102ڡ 17:34:19 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42480
ޤ륱
#42473 ȯοȯǡ
[0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 120, 121, 243, 244, 246, 247, 252, 253, 255, 256, 271, 279, 280, 283, 284, 291, 293, 294, 300, 301, 607, 608, 610, 611, 616, 617, 619, 620, 634, 635, 637, 638, 643, 644, 646, 647, 688, 689, 691, 692, 697, 698, 700, 701, 715, 716, 718, 719, 724, 725, 727, 728]
82Υѥȯ
ϡץήäѤʤǵޤ
ʤ硡 102ڡ 17:42:28 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42481
ʪ
0,1,3,4,9򤷤Ф餯Ƥߤ
3n褬Ф
ޤǤοι2n+1
729=36
729ޤǤ65
728ޤǤ64ࡣ
ܡ 102ڡ 18:02:50 42482
̴
ʬ餺ͼ򳫤ȡޥ뤵󤬣ˡȽ񤤤ƲäƤäǤϡʬꡢ64ˤé夤ΤǤ
ٻΤ桡 102ڡ 21:50:55 42483
ʪ
0֤728ޤĴ٤Ƥä
뤳ȤǽʿФƤϤʤ褦ˤ
#42482βˡǺ礬ȤϤǤ
ܡ 102ڡ 22:53:31 42484

#42480η̡27礫11ѥˤˤäơ729礫ϤȤаʲΤ褦ˤ88ѥޤ

[0, 2, 6, 8, 18, 20, 24, 26] * 27 + [0, 1, 5, 6, 8, 14, 18, 19, 21, 25, 26]

81礫22ѥ󡢤Ȥ
[0, 2] * 27 + [0, 1, 5, 6, 8, 14, 18, 19, 21, 25, 26]
뤳Ȥ狼ޤ23ʰʾˤΥѥ¸ߤ뤫ˤʤޤʸĤ729Ф92ʰʾˤΥѥ
Ȥ櫓81Фõץ餻ƤߤƤޤ22ѥݥĥݥĸĤФǡ23ѥϤޤĤäƤޤ󡣤ޤǤΤȤͤȤ֤󤢤Ǥ礦ɡ

ɵ
ͽۤȿơɤ81Ф23ѥϤʤ褦Ǥ
080 ʶA026ˡʶB2753ˡʶC5480ˤ3֤ʬơʳƶ֤Ϻ11ޤǡˡAޤC Τ줫 11礢ѥ10礢ѥ󡢡ġġ6礢ѥ󡢤ȽõƤߤޤĤޤǤ
Ȥʤȼ243礫44Ķѥ뤫ġĤʤΤǤ˥ץǤ⸷ޤ
103ʶ 3:01:45 42485
Halt0
ͤˤĤƥץꤷΤˤƸƤߤȤ,
缭ŵA003002ꤽΤΤǤ. https://oeis.org/A003002
"Size of the largest subset of the numbers [1...n] which does not contain a 3-term arithmetic progression."

Ȥ"More terms of this sequence can be found directly from A065825"Ȥޤ.
A065825ȤΤϤ. https://oeis.org/A065825
"Smallest k such that n numbers may be picked in {1,...,k} with no three terms in arithmetic progression."

פ, ξ, A065825 ο a(n) ȤȤ, a(n)729 ˤʤ褦ʺǾ n Ф ( n-1 ˤʤ) 櫓ǤĸߤΤȤ, ΤƤΤϤɤ a(41)=194 ޤǤߤǤ. http://www.math.uni.wroc.pl/~jwr/non-ave.htm ˤ, ͤΤ 2.8 GHz CPU 11.5 ֤äǤ. ͤޤǤ.
104ڡ 4:18:03 42486

Halt0#42486ζƤäȤˤ a(45)227 ȤΤȤʤΤǡ227(<243)45ѥϺǤ͡
Ȥ 681 (<729) 90ѥ뤳ȤǤޤ

90 狼³Ǥ礦ġ
104ڡ 5:32:26 42487
Ȼ
#42487 󤵤󡡡a(45)227 ʤ680礸ʤǤ礦
104ڡ 12:29:21 42488
uchinyan
#42480#42481#42485#42486#42487
Ūʥץ񤷤äΤǥץåͻҤ򸫤ƤΤǤ
#42486ͻҤǤΤ褦Ǥ͡

#42485ιͤˤäơʬΤ˾ޤȤƤȡΤ褦ˤʤΤǤ礦

0 3^n - 1 κ c(n) ȤС0 3^(n+1) - 1 c(n+1) ϡ
0 3^(n+1) - 1
0 3^n - 13^n 2 * 3^n - 12 * 3^n 3^(n+1) - 1λĤζ֤ʬơ
0 3^n - 1 ˤϡ0 3^n - 1 βΰĤ򤽤Τޤ
2 * 3^n 3^(n+1) - 1 ˤϡ0 3^n - 1 βΰĤγơο 2 * 3^n ­
3^n 2 * 3^n - 1 ˤϡ0 3^n - 1 2 * 3^n 3^(n+1) - 1 οʿѤˤʤʤ
褦ˤСդΤơΤȤ
0 3^n - 1 c(n)2 * 3^n 3^(n+1) - 1 c(n)3^n 2 * 3^n - 1 d(n) ȤС
c(n+1) >= 2 * c(n) + d(n)
ˤʤޤ
ϡ d(n) Ǥץˤ¸Ǥϡ
c(n+1) = 2 * c(n) + d(n)d(n) = 0 1
ȤʤꤽǤ͡


0 3^n - 1 ˤϡ0 3^n - 1 βΰĤ򤽤Τޤ
2 * 3^n 3^(n+1) - 1 ˤϡ0 3^n - 1 줿ΤƱ
ȤС3^n 2 * 3^n - 1 ˤ줺 d(n) = 0 ˤʤޤ
ˤ뤳ȤˤˤС
c(n+1) = 2 * c(n)c(n) = 2^n
ϥޥ뤵δԤƤͽ۲ǺνΥ١ˤʤäΤǡ3 ˡ᤬ưפǤ
ºݤˤϡषä褦Ǥ

⤷2 * 3^n 3^(n+1) - 1 Ĵƾ d(n) = 1 ȤǤ椬ˤʤʤС
c(n+1) = 2 * c(n) + 1c(n) = 3 * 2^(n-1) - 1
ϡn = 1, 2, 3 Ǥ#42485Τ󤵤κǽͽۤǤ
ʹߤϤ꾮ʤ褦Ǥϡd(n) = 0 롤¿ 0̣ޤ
ĤޤꡤǤϤʤޤǤκޤǤΥץǤμ¸ͽۤǤ
ͤϡ峦ΰĤΤ褦Ǥ
ʤߤˡξ 0 728 ФΤ c(6) = 95 Ǥ

ˡ
n = 1, 2, 3c(n+1) = 2 * c(n) + 1n >= 4c(n+1) = 2 * c(n)
Ȳꤹȡ
n = 1, 2, 3c(n) = 3 * 2^(n-1) - 1n >= 4c(n+1) = 11 * 2^(n-3)
Ȥʤꡤ0 728 ФΤ c(6) = 88 Ȥʤꡤ#42485κǽȰפޤ

ʤ顤#42487ˤ 90 ǽȤȤʤΤǡ
ɤǥݥĥݥĤ d(n) = 1 ˤʤΤȻפޤ
ȤۤʤѥʤΤǤ礦
ͥνȡ 104ڡ 14:45:30 42489

Ȼ#42488ΤäȤǤ
3ʿ3ʬǹͤΤäƤơ֤Υåʬ 1 ͤ뤳ȤǤΤȤƤޤ

uchinyan#42489
֤ޤפդޤȤ
d(1)=d(2)=1, d(3)=0, d(4)1, d(5)=? ȤȤǤ͡
68090ʤ顢49ΥڡǤ⤦1ȤȤǤġ

104ڡ 18:54:00 42490
Halt0
http://www.math.uni.wroc.pl/~jwr/non-ave/ 򹹤˸ƤߤȤ,

http://www.math.uni.wroc.pl/~jwr/non-ave/DATABASE.TXT
a(93)<=676 1 2 8 11 13 16 22 23 27 29 49 51 54 55 65 67 68 74 77 78 84 98 130 136 144 149 156 159 161 164 170 171 175 177 197 199 202 203 213 215 216 222 225 226 232 246 278 284 440 445 452 455 457 460 466 467 471 473 493 495 498 499 509 511 512 518 521 522 528 542 574 580 588 593 600 603 605 608 614 615 619 621 641 643 646 647 657 659 660 666 669 670 676 (1095251260 Gavin Theobald)

ȤΤȤ 93 ϲǽ.

http://www.math.uni.wroc.pl/~jwr/non-ave/BEST.TXT 򸫤, ɤ a(96)<=709 Theorem 24 ˤäƤ狼äƤäݤǤ (֤), ŪˤɤΤ褦˽ɽΤϤ褯狼ޤ. Theorem 24 ȤΤ http://www.math.uni.wroc.pl/~jwr/non-ave/methods.htm Theorem N ΤȤߤǤ, ɤΤ褦ƳΤ, ɤäŬѤΤ, ˤϤ褯狼ޤǤ.


ҤͤⲿʤǤ Gavin Theobald η̤ 690 722 728 դä 96 ˤǤΤ, Ȥꤢ a(96)<=728 Ǥ. a(97) ˴ؤƤ̤ a(97)<=736 ޤǤ狼äƤʤäݤΤ (Ȥ736դäФΩ) θ³96Ȼפޤ.

104ڡ 20:23:00 42491

Halt0#42491
a(96)709 ȤΤϡTheorem N ˤ N=24,q=4,r=24 ȤߤǤ

N=24 ФƤ modular solution m(24)148 P=148
{k_1 ġ k_24} = {0 6 14 19 26 29 31 34 40 41 45 47 67 69 72 73 83 85 86 92 95 96 102 116} + 1
ޤ
a(4)=5, k_24=117 Ǥ
Theorem N μ

a(24*(4-1)+24) 148*(5-1)+117

a(96)709 ޤ
äݤʤΤϡTheorem N ˻Ȥ modular solution {k_r} http://www.math.uni.wroc.pl/~jwr/non-ave/DATABASE.TXT ˤΤ򤽤Τޤ޻ȤΤǤϤʤ(1) ٤ 1ʾˤʤ褦ˡ(2) Ȥ k_r Ǿˤʤ褦ˡmod P Ŭ˥ơ󤹤ȤȤǤʾξ 1 äǴñǤ

modular solution ȤΤϡΤ褦ξüä֤ΤˡξüĤʤäƼ֤ˤʬޤޤʤͤΤǤ
Ȥо {k_r} 0147 μŪ־ǡʬޤޤʤǤ

ɵ
Theorem N ιͤϡmodular solution Ŭʥå׶֤ϤߤʤĤʤǤȤ¤ϤʤꥷץʤΤǤ
Ȥо a(96) ξϡ

[M24(148)][M24(148)][å(148)][M24(148)][M24Ƭʬ(117)]
M24 modular solution, ()϶Ĺ

ˤä a(96) бäƤޤ
modular solution ȤȤǡȤʤꤢ֤ǴĤä󤬽иΤɤǤޤ
ޤΤι¤ a(4) б {0,1,3,4} ǷޤäƤꡢ3Ĥζ֤ޤ󤬽иʤ褦ˤƤޤ
104ڡ 23:27:53 42492
Halt0
#42492
, ȤǤ. ꤬Ȥޤ. ɤ modular solution 򴪰㤤ƤäݤǤ.
Ĥޤ,

{0 6 14 19 26 29 31 34 40 41 45 47 67 69 72 73 83 85 86 92 95 96 102 116} + 1 + 148*({1 2 4 5} - 1)
={1 7 15 20 27 30 32 35 41 42 46 48 68 70 73 74 84 86 87 93 96 97 103 117 149 155 163 168 175 178 180 183 189 190 194 196 216 218 221 222 232 234 235 241 244 245 251 265 445 451 459 464 471 474 476 479 485 486 490 492 512 514 517 518 528 530 531 537 540 541 547 561 593 599 607 612 619 622 624 627 633 634 638 640 660 662 665 666 676 678 679 685 688 689 695 709}

a(96) ξ峦ƤΤǤ. ʤۤ.
( modular solution x,y ȤäƤȤ (x+y)/2 + 74 modular solution ˴ޤޤƤȤޤɤβǽϤʤΤġ ʤɤǺǤޤޤ,
x, (x+y)/2+74, y mod 148 ˤʤ뤫饢ȤǤ. ʿѤȤդ˰ŤƤ)
ȥåץڡ"Note that if m(n) is even, then terms i and i+m(n)/2 exclude each other. "Ƚ񤫤Ƥ뤳Ȥˤޤ.

106ʷ 4:05:37 42493
uchinyan
#42491#42492#42493
󶡤Ȳ򤢤꤬Ȥޤ
աࡤȾʬʬä褦Ǽ¤ʬäƤʤʡȤϻפΤΡäήϡʤۤɡȤǤ

ɤΤȤ96 ϤǤ롤97 ϸߤϲǽʬʤ¿ʬ̵ȤȤǤ礦

#42489ǡ٤Ƥ d(n) 1 95 峦ʤͽۤΩƤޤˤϤޤ
n 礭ʤз֤¿ʤΤ d(n) 礭ʤäƤԻ׵ĤϤʤ櫓Ǥ
⤽ñʣʬ䤫ϤȤǡ⤷ä顤ȤβǤɾʤΤǡ
ϤƤǤ͡
ºݡa(96) ιϡ褦ʹͤΤ褦Ǥ̲줿ΤΤ褦Ǥ͡

ٶˤʤޤ

ѤäǤ

ϽԤΰտޤϤ뤫ĶƤޤäǤϼԺȸ虜ʤǤ礦
͡ʿθ줿Ǥ礭ʼϤޤ
ΥȤϡ¾ΥȤȰäơ򤤤ƽꡤǤϤʤߤΤ¿Τǡ
ȹͻǤƳڤǤ֤Ȥ֤礦ɤ褦˻פޤ

ޥ뤵󡤤줫ڤߤˤƤޤ͡
ͥνȡ 105 12:14:22 MAIL:uchi@sco.bekkoame.ne.jp 42495
ޥ
ϤǤ򤪤ޤ󡣤õפϤߤʤǤä...ߤޤ

ͤϡõβڤǤä褦ǤϤϤäƤϤʤʤȤǤʤ줬äѤʤȤǤ...

ϤʤϤǤν񤭹ߤäȳڤɤǤꤷޤʤߤޤ..˺Ȥ⡢ꤤޤϿޤǤm(__)m
MacbookPro 105 20:03:24 HomePage:42496
ʪ
9697ϤɤʤΤǤ礦
ϾǤǤʤǤ礦͡
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