[seqfan] Re: How to list pairs, triples, etc.

[Hans Havermann]

  Richard Guy:

> Well, that went up like a lead balloon!  No-one noticed
> the triples  {159,130,66}  {160,129,96}  {182,107,14},
> {190,134,35}  and  {192,132,64}  showing that I missed
> 159, 160, 182, 190 and 192 from the sequence.  How many
> others did I miss?

I hadn't even looked at your largest-triplet list because I've been  
working on finding the largest number for which there are NO solutions  
as a largest-triplet (that result in a few hours). But I do have a  
small list of solutions which I'll share now:

{30, 19, 6}
{44, 20, 5}
{47, 34, 2}
{48, 33, 16}
{60, 21, 4}
{66, 34, 15}
{69, 52, 12}
{70, 51, 30}
{78, 22, 3}
{86, 35, 14}
{90, 54, 10}
{92, 52, 29}
{94, 75, 6}
{95, 74, 26}
{96, 73, 48}
{98, 23, 2}
{108, 36, 13}
{113, 56, 8}
{116, 53, 28}
{118, 78, 3}
{120, 24, 1}
{120, 76, 24}
{122, 74, 47}
{124, 101, 20}
{125, 100, 44}
{126, 99, 70}
{132, 37, 12}
{138, 58, 6}
{142, 54, 27}
{147, 78, 22}
{150, 75, 46}
{152, 104, 17}
{154, 102, 42}
{156, 100, 69}
{157, 132, 12}
{158, 38, 11}
{158, 131, 38}
{159, 130, 66}
{160, 129, 96}
{165, 60, 4}
{170, 55, 26}
{176, 80, 20}
{180, 76, 45}
{182, 107, 14}
{185, 104, 40}
{186, 39, 10}
{188, 136, 8}
{188, 101, 68}
{190, 134, 35}
{192, 132, 64}
{194, 62, 2}
{194, 167, 2}
{194, 130, 95}
{195, 166, 30}
{196, 165, 60}
{197, 164, 92}
{198, 163, 126}
{200, 56, 25}
{207, 82, 18}
{212, 77, 44}
{214, 110, 11}
{216, 40, 9}
{218, 106, 38}
{221, 140, 4}
{222, 102, 67}
{224, 137, 32}
{227, 134, 62}
{230, 170, 26}
{230, 131, 94}
{232, 57, 24}
{232, 168, 57}
{234, 166, 90}
{236, 205, 20}
{236, 164, 125}
{237, 204, 52}
{238, 203, 86}
{239, 202, 122}
{240, 84, 16}
{240, 201, 160}
{246, 78, 43}
{248, 41, 8}
{248, 113, 8}
{253, 108, 36}
{258, 103, 66}
{260, 140, 29}
{264, 136, 60}
{266, 58, 23}
{267, 174, 22}
{268, 132, 93}
{270, 171, 54}
{273, 168, 88}
{274, 210, 15}
{275, 86, 14}
{276, 208, 48}
{276, 165, 124}
{278, 206, 83}
{280, 204, 120}
{281, 248, 8}
{282, 42, 7}
{282, 79, 42}
{282, 247, 42}
{282, 202, 159}
{283, 246, 78}
{284, 116, 5}
{284, 245, 116}
{285, 244, 156}
{286, 243, 198}
{290, 110, 34}
{296, 104, 65}
{298, 143, 26}
{302, 59, 22}
{303, 138, 58}
{306, 178, 18}
{308, 133, 92}
{310, 174, 51}
{312, 88, 12}
{314, 215, 10}
{314, 170, 86}
{317, 212, 44}
{318, 43, 6}
{318, 166, 123}
{320, 80, 41}
{320, 209, 80}
{322, 119, 2}
{322, 254, 2}
{323, 206, 118}
{324, 252, 37}
{326, 250, 74}
{326, 203, 158}
{328, 248, 113}
{329, 112, 32}
{330, 246, 154}
{331, 294, 30}
{332, 293, 68}
{332, 244, 197}
{333, 292, 108}
{334, 291, 150}
{335, 290, 194}
{336, 105, 64}
{336, 289, 240}
{338, 146, 23}
{340, 60, 21}
{344, 140, 56}
{347, 182, 14}
{350, 134, 91}
{351, 90, 10}
{352, 177, 48}
{356, 44, 5}
{356, 220, 5}
{357, 172, 84}
{360, 81, 40}
{360, 216, 40}
{362, 167, 122}
{364, 212, 77}
{368, 257, 32}
{368, 208, 116}
{370, 114, 30}
{371, 254, 70}
{372, 204, 157}
{374, 251, 110}
{376, 300, 24}
{377, 248, 152}
{378, 106, 63}
{378, 298, 63}
{380, 61, 20}
{380, 149, 20}
{380, 296, 104}
{380, 245, 196}
{382, 294, 147}
{384, 345, 16}
{384, 292, 192}
{385, 344, 56}
{386, 343, 98}
{386, 290, 239}
{387, 142, 54}
{387, 342, 142}
{388, 341, 188}
{389, 340, 236}
{390, 186, 10}
{390, 339, 286}
{392, 92, 8}
{394, 135, 90}
{396, 45, 4}
{396, 180, 45}
{402, 82, 39}
{402, 174, 82}
{405, 220, 36}
{408, 168, 121}
{410, 215, 74}
{413, 116, 28}
{414, 262, 27}
{415, 210, 114}
{418, 258, 66}
{420, 205, 156}
{422, 62, 19}
{422, 107, 62}
{422, 254, 107}
{423, 306, 18}
{424, 152, 17}
{426, 303, 58}
{426, 250, 150}
{429, 300, 100}
{430, 246, 195}
{432, 352, 9}
{432, 144, 52}
{432, 297, 144}
{434, 350, 50}
{435, 94, 6}
{435, 190, 6}
{435, 294, 190}
{436, 348, 93}
{438, 46, 3}
{438, 346, 138}
{438, 291, 238}
{440, 136, 89}
{440, 344, 185}
{442, 183, 42}
{442, 399, 42}
{442, 342, 234}
{443, 398, 86}
{444, 397, 132}
{444, 340, 285}
{445, 396, 180}
{446, 83, 38}
{446, 395, 230}
{447, 394, 282}
{448, 393, 336}
{449, 176, 80}
{452, 224, 32}
{456, 169, 120}
{458, 118, 26}
{458, 218, 71}
{462, 267, 22}
{464, 212, 112}
{466, 63, 18}
{467, 262, 62}
{468, 108, 61}
{470, 155, 14}
{470, 206, 155}
{472, 312, 12}
{472, 257, 104}
{476, 308, 53}
{477, 252, 148}
{479, 146, 50}
{480, 96, 4}
{480, 304, 96}
{482, 47, 2}
{482, 194, 2}
{482, 359, 2}
{482, 247, 194}
{484, 300, 141}
{485, 356, 44}
{488, 137, 88}
{488, 353, 88}
{488, 296, 188}
{490, 186, 39}
{491, 350, 134}
{492, 84, 37}
{492, 292, 237}
{494, 406, 35}
{494, 347, 182}
{496, 404, 80}
{497, 344, 232}
{498, 178, 78}
{498, 402, 127}
{500, 400, 176}
{500, 341, 284}
{501, 228, 28}
{502, 398, 227}
{503, 458, 26}
{504, 457, 72}
{504, 396, 280}
{505, 120, 24}
{505, 456, 120}
{506, 170, 119}
{506, 455, 170}
{506, 394, 335}
{507, 454, 222}
{508, 221, 68}
{508, 453, 276}
{509, 452, 332}
{510, 451, 390}
{512, 64, 17}
{512, 272, 17}
{515, 214, 110}
{516, 109, 60}
{518, 158, 11}
{518, 266, 58}
{522, 207, 154}
{523, 318, 6}
{524, 260, 101}
{527, 98, 2}
{528, 48, 1}
{528, 148, 48}
{528, 313, 48}
{530, 254, 146}
{533, 308, 92}
{536, 248, 193}
{538, 362, 38}
{538, 138, 87}
{538, 303, 138}
{540, 85, 36}
{540, 189, 36}
{542, 358, 83}
{543, 298, 186}
{546, 354, 130}
{548, 413, 28}
{548, 293, 236}
{549, 180, 76}
{550, 350, 179}
{551, 410, 74}
{552, 232, 24}
{554, 122, 22}
{554, 407, 122}
{554, 346, 230}
{557, 404, 172}
{558, 466, 18}
{558, 171, 118}
{558, 342, 283}
{560, 65, 16}
{560, 224, 65}
{560, 464, 65}
{560, 401, 224}
{562, 462, 114}
{563, 398, 278}
{564, 277, 12}
{564, 460, 165}
{566, 110, 59}
{566, 458, 218}
{566, 395, 334}
{568, 161, 8}
{568, 521, 8}
{568, 216, 108}
{568, 456, 273}
{569, 520, 56}
{570, 519, 106}
{570, 454, 330}
{571, 270, 54}
{571, 518, 158}
{572, 517, 212}
{572, 452, 389}
{573, 516, 268}
{574, 515, 326}
{575, 514, 386}
{576, 208, 153}
{576, 513, 448}
{578, 263, 98}
{579, 150, 46}
{582, 318, 43}
{585, 256, 144}
{588, 312, 88}
{590, 86, 35}
{590, 139, 86}
{592, 192, 33}
{592, 249, 192}
{593, 368, 32}
{594, 306, 135}
{598, 363, 78}
{600, 300, 184}
{602, 182, 74}
{603, 358, 126}
{604, 420, 21}
{605, 124, 20}
{605, 236, 20}
{606, 294, 235}
{608, 416, 68}
{608, 353, 176}
{610, 66, 15}
{612, 172, 117}
{612, 412, 117}
{613, 348, 228}
{614, 227, 62}
{615, 474, 10}
{616, 408, 168}
{618, 282, 7}
{618, 111, 58}
{618, 471, 58}
{618, 343, 282}
{620, 164, 5}
{620, 404, 221}
{621, 468, 108}
{623, 218, 106}
{624, 465, 160}
{624, 400, 276}
{626, 274, 50}
{627, 462, 214}
{628, 528, 48}
{628, 396, 333}
{630, 526, 99}
{630, 459, 270}
{632, 152, 44}
{632, 209, 152}
{632, 524, 152}
{633, 456, 328}
{634, 266, 95}
{634, 522, 207}
{636, 520, 264}
{636, 453, 388}
{638, 323, 38}
{638, 587, 38}
{638, 518, 323}
{639, 586, 90}
{640, 585, 144}
{640, 516, 384}
{641, 584, 200}
{642, 87, 34}
{642, 258, 142}
{642, 583, 258}
{642, 514, 447}
{643, 582, 318}
{644, 140, 85}
{644, 581, 380}
{645, 316, 84}
{645, 580, 444}
{646, 195, 30}
{646, 579, 510}
{650, 374, 26}
{650, 250, 191}
{652, 309, 132}
{656, 368, 73}
{657, 184, 72}
{658, 126, 18}
{659, 302, 182}
{660, 240, 16}
{662, 67, 14}
{662, 427, 14}
{662, 362, 122}
{666, 295, 234}
{667, 422, 62}
{668, 173, 116}
{668, 356, 173}
{670, 230, 59}
{672, 112, 57}
{672, 417, 112}
{674, 167, 2}
{674, 287, 2}
{674, 482, 2}
{674, 350, 226}
{677, 412, 164}
{678, 478, 51}
{680, 220, 104}
{680, 344, 281}
{682, 474, 102}
{682, 407, 218}
{683, 278, 46}
{686, 470, 155}
{687, 154, 42}
{687, 402, 274}
{689, 536, 40}
{690, 210, 151}
{690, 466, 210}
{692, 269, 92}
{692, 533, 92}
{692, 397, 332}
{694, 462, 267}
{695, 530, 146}
{696, 88, 33}
{696, 328, 33}
{698, 527, 202}
{698, 458, 326}
{700, 596, 29}
{700, 141, 84}
{701, 260, 140}
{701, 524, 260}
{702, 198, 27}
{702, 594, 82}
{702, 454, 387}
{704, 320, 80}
{704, 592, 137}
{704, 521, 320}
{706, 590, 194}
{707, 518, 382}
{708, 588, 253}
{709, 380, 20}
{710, 251, 190}
{710, 586, 314}
{710, 515, 446}
{711, 658, 18}
{712, 657, 72}
{712, 312, 129}
{712, 584, 377}
{713, 128, 16}
{713, 656, 128}
{714, 186, 70}
{714, 655, 186}
{714, 582, 442}
{715, 654, 246}
{716, 68, 13}
{716, 373, 68}
{716, 653, 308}
{716, 580, 509}
{717, 244, 12}
{717, 652, 372}
{718, 651, 438}
{719, 650, 506}
{720, 304, 180}
{720, 649, 576}
{722, 434, 7}
{723, 366, 118}
{726, 174, 115}
{728, 113, 56}
{728, 233, 56}
{728, 428, 56}
{728, 296, 233}
{730, 359, 170}
{734, 422, 107}
{737, 352, 224}
{739, 222, 102}
{740, 485, 44}
{740, 416, 160}
{742, 282, 42}
{744, 156, 40}
{744, 345, 280}
{745, 480, 96}
{746, 410, 215}
{750, 211, 150}
{750, 475, 150}
{752, 89, 32}
{752, 544, 32}
{752, 272, 89}
{752, 404, 272}
{755, 470, 206}
{756, 333, 28}
{756, 540, 85}
{758, 142, 83}
{758, 398, 331}
{760, 201, 24}
{760, 536, 140}
{760, 465, 264}
{762, 262, 138}
{764, 605, 20}
{764, 532, 197}
{765, 324, 76}
{765, 460, 324}
{767, 602, 74}
{768, 528, 256}
{770, 130, 14}
{770, 386, 14}
{770, 599, 130}
{770, 455, 386}
{772, 69, 12}
{772, 252, 189}
{772, 524, 317}
{773, 188, 68}
{773, 596, 188}
{774, 315, 126}
{776, 248, 8}
{776, 668, 8}
{776, 593, 248}
{776, 520, 380}
{778, 378, 63}
{778, 666, 63}
{779, 590, 310}
{780, 664, 120}
{780, 516, 445}
{782, 662, 179}
{782, 587, 374}
{783, 306, 178}
{784, 660, 240}
{785, 584, 440}
{786, 114, 55}
{786, 175, 114}
{786, 370, 114}
{786, 658, 303}
{788, 236, 53}
{788, 656, 368}
{788, 581, 508}
{789, 732, 52}
{790, 731, 110}
{790, 654, 435}
{791, 434, 50}
{791, 730, 170}
{792, 297, 232}
{792, 729, 232}
{792, 652, 504}
{793, 728, 296}
{794, 362, 167}
{794, 727, 362}
{794, 650, 575}
{795, 726, 430}
{796, 725, 500}
{797, 724, 572}
{798, 427, 102}
{798, 723, 646}
{800, 224, 100}
{802, 354, 222}
{803, 158, 38}
{803, 286, 38}
{804, 492, 37}
{805, 420, 156}
{810, 90, 31}
{810, 486, 90}
{810, 346, 279}
{812, 212, 149}
{812, 413, 212}
{814, 275, 86}
{816, 480, 145}
{817, 552, 24}
{818, 338, 23}
{818, 143, 82}
{819, 406, 270}
{820, 204, 21}
{822, 547, 78}
{822, 474, 202}
{825, 264, 136}
{826, 399, 330}
{827, 542, 134}
{828, 328, 72}
{828, 468, 261}
{829, 132, 12}
{830, 70, 11}
{830, 614, 11}
{832, 537, 192}
{833, 392, 8}
{834, 190, 66}
{834, 610, 66}
{834, 462, 322}
{836, 253, 188}
{837, 252, 4}
{837, 532, 252}
{838, 318, 123}
{838, 606, 123}
{840, 456, 385}
{842, 383, 58}
{842, 602, 182}
{842, 527, 314}
{846, 115, 54}
{846, 675, 54}
{846, 598, 243}
{847, 522, 378}
{848, 176, 113}
{848, 308, 176}
{849, 672, 112}
{850, 239, 50}
{850, 594, 306}
{851, 374, 110}
{852, 669, 172}
{852, 517, 444}
{854, 590, 371}
{855, 666, 234}
{856, 440, 44}
{858, 742, 42}
{858, 298, 231}
{858, 663, 298}
{858, 586, 438}
{860, 740, 101}
{860, 365, 164}
{861, 660, 364}
{862, 738, 162}
{862, 582, 507}
{863, 226, 98}
{864, 160, 36}
{864, 432, 97}
{864, 736, 225}
{864, 657, 432}
{866, 290, 34}
{866, 734, 290}
{867, 654, 502}
{868, 732, 357}
{869, 356, 220}
{870, 91, 30}
{870, 499, 30}
{870, 811, 30}
{870, 730, 426}
{870, 651, 574}
{871, 810, 90}
{872, 424, 152}
{872, 809, 152}
{872, 728, 497}
{873, 808, 216}
{874, 807, 282}
{874, 726, 570}
{875, 806, 350}
{876, 213, 148}
{876, 805, 420}
{876, 724, 645}
{877, 492, 84}
{877, 804, 492}
{878, 278, 83}
{878, 347, 278}
{878, 803, 566}
{879, 802, 642}
{880, 144, 81}
{880, 416, 209}
{880, 801, 720}
{882, 207, 18}
{882, 343, 18}
{884, 560, 16}
{884, 485, 140}
{888, 408, 268}
{890, 71, 10}
{890, 134, 10}
{890, 554, 71}
{890, 266, 134}
{891, 478, 198}
{893, 332, 68}
{896, 548, 128}
{896, 400, 329}
{897, 192, 64}
{898, 398, 2}
{898, 623, 2}
{898, 471, 258}
{902, 254, 187}
{902, 542, 187}
{903, 618, 58}
{904, 321, 120}
{905, 464, 320}
{908, 116, 53}
{908, 388, 53}
{908, 613, 116}
{908, 536, 248}
{912, 177, 112}
{912, 457, 384}
{913, 608, 176}
{914, 242, 47}
{914, 530, 311}
{915, 310, 174}
{916, 684, 45}
{918, 378, 106}
{918, 603, 238}
{920, 680, 104}
{920, 524, 376}
{923, 446, 38}
{923, 598, 302}
{924, 676, 165}
{926, 299, 230}
{926, 518, 443}
{927, 162, 34}
{928, 228, 96}
{928, 368, 161}
{928, 672, 228}
{928, 593, 368}
{929, 752, 32}
{931, 294, 30}
{932, 92, 29}
{932, 437, 92}
{932, 749, 92}
{932, 668, 293}
{933, 588, 436}
{935, 746, 154}
{936, 664, 360}
{938, 506, 23}
{938, 358, 218}
{938, 743, 218}
{938, 583, 506}
{940, 660, 429}
{941, 428, 148}
{941, 740, 284}
{942, 822, 19}
{942, 214, 147}
{944, 145, 80}
{944, 281, 80}
{944, 820, 80}
{944, 737, 352}
{944, 656, 500}
{946, 210, 15}
{946, 498, 78}
{946, 818, 143}
{947, 734, 422}
{948, 348, 13}
{948, 816, 208}
{948, 348, 277}
{948, 652, 573}
{950, 419, 206}
{950, 814, 275}
{950, 731, 494}
{952, 72, 9}
{952, 812, 344}
{953, 136, 8}
{953, 568, 8}
{953, 728, 568}
{954, 490, 135}
{954, 810, 415}
{955, 894, 6}
{956, 893, 68}
{956, 808, 488}
{956, 725, 644}
{957, 268, 132}
{957, 892, 132}
{958, 891, 198}
{958, 806, 563}
{959, 410, 266}
{959, 890, 266}
{960, 336, 64}
{960, 561, 64}
{960, 889, 336}
{960, 804, 640}
{961, 888, 408}
{962, 194, 62}
{962, 482, 194}
{962, 887, 482}
{962, 802, 719}
{963, 886, 558}
{964, 885, 636}
{965, 884, 716}
{966, 883, 798}
{967, 554, 122}
{968, 401, 328}
{970, 255, 186}
{970, 474, 255}
{972, 117, 52}
{972, 324, 117}
{974, 626, 50}
{974, 547, 182}
{976, 393, 48}
{978, 178, 111}
{978, 466, 318}
{980, 245, 44}
{980, 620, 109}
{981, 540, 244}
{984, 312, 172}
{986, 614, 170}
{986, 458, 383}
{987, 382, 102}
{988, 693, 36}
{988, 533, 308}
{992, 164, 32}
{992, 452, 32}
{992, 608, 233}
{993, 688, 96}
{995, 230, 94}
{995, 526, 374}
{996, 93, 28}
{996, 300, 229}
{998, 298, 26}
{998, 371, 158}
{998, 683, 158}
{998, 602, 298}