The first differences of S

are the semi-prime numbers of S

De : Alois Heinz

Envoyé : samedi 11 décembre 2010 0:10

À : Eric Angelini

Objet : Re: [seqfan] Re: The first differences of S are the prime numbers of S

Dear Eric,

Here is another list you might like, the FirstDiffSemiPrimes:

SP = 1, 5, 11, 2, 12, 27, 13, 47, 8, 29, 3, 28, 50, 4, 37, 72, 7, 45, 96, 19, 68, 6, 61, 130, 9, 66, 124, 18, 92, 10, 97, 182, 16, 102, 193, 15, 108, 14, 109, 220, 17, 132, 250, 24, 147, 266, 31, 153, 20, 149, 283, 30, 171, 313, 48, 191, 32, 190, 44, 189, 34, 195, 364, 23, 200, 383, 54, 239, 52, 246, 40, 241, 36, 238, 452, 39, 248, 461, 63, 280, 21, 236, 455, 60, 281, 499, 26, 263, 510, 25, 279, 528, 59, 333, 42, 304, 571, 56, 343, 22, 300, 595, 41, 330, 628, 75, 374, 71, 372, 46, 348, 43, 352, 33, 347, 670, 35, 369, 696, 67, 402, 741, 70, 416, 774, 53, 408, 769, 80, 442, 65, 430, 801, 38, 419, 805, 88, 470, 76, 467, 64, 457, 864, 51, 462, 877, 78, 495, 73, 500, 937, 99, 544, 90, 536, 83, 530, 79, 550, 84, 577, 1035, 77, 555, 1036, 81, 563, 49, 546, 1048, 89, 578, 1083, 98, 599, 62, 588, 55, 572, 1091, 112, 639, 101, 612, 69, 598, 1140, 103, 638, 1183, 104, 663, 1225, 110, 661, 1240, 105, 678, 113, 702, 116, 682, 1265, 100, 691, 1272, 125, 722, 1336, 117, 728, 1350, 107, 730, 1356, 151, 784, 135, 790, 121, 783, 1450, 57, 736, 1370, 136, 810, 1491, 120, 814, 127, 812, 114, 809, 1506, 137, 836, 58, 761, 1467, 128, 846, 139, 852, 106, 829, 74, 808, 1539, 82, 819, 1564, 87, 840, 1598, 85, 834, 1600, 131, 902, 1669, 140, 919, 126, 907, 1692, 154, 945, 138, 927, 1721, 144, 946, 1749, 160, 975, 157, 988, 1805, 150, 991, 148, 983, 1825, 152, 1001, 1852, 163, 1025, 156, 1021, 1887, 170, 1049, 1920, 166, 1044, 1930, 164, 1053, 1946, 165, 1060, 86, 984, 1885, 167, 1066, 1971, 168, 1085, 162, 1075, 1989, 172, 1093, 2015, 174, 1100, 2034, 91, 1024, 1973, 176, 1127, 184, 1123, 2084, 175, 1148, 2113, 179, 1161, 2150, 173, 1166, 2161, 178, 1176, 2179, 188, 1194, 93, 1104, 2111, 192, 1210, 2237, 186, 1228, 181, 1222, 2265, 94, 1151, 2197, 95, 1150, 2223, 197, 1256, 111, 1178, 2255, 196, 1277, 2371, 180, 1279, 2390, 204, 1323, 2405, 199, 1320, 2457, 208, 1334, 2448, 203, 1341, 115, 1248, 2387, 198, 1340, 2494, 211, 1352, 2511, 232, 1381, 118, 1275, 2442, 223, 1392, 2583, 222, 1396, 207, 1384, 2570, 228, 1423, 212, 1410, 2609, 240, 1442, 2645, 210, 1424, 2662, 216, 1443, 2650, 224, 1471, 230, 1483, 226, 1481, 2742, 225, 1487, 2754, 123, 1394, 2667, 233, 1515, 229, 1523, 2808, 227, 1520, 119, 1425, 2724, 235, 1548, 231, 1549, 234, 1556, 2889, 251, 1580, 243, 1586, 2932, 271, 1616, 261, 1608, 122, 1476, 2825, 252, 1609, 258, 1621, 242, 1624, 2990, 244, 1627, 3012, 255, 1644, 257, 1648, 245, 1647, 133, 1530, 2945, 264, 1675, 129, 1534, 2952, 134, 1551, 2988, 253, 1694, 256, 1710, 141, 1602, 3067, 260, 1733, 142, 1620, 3121, 275, 1741, 3243, 265, 1772, 3289, 272, 1794, 143, 1640, 3167, 268, 1777, 159, 1696, 3231, 158, 1699, 3260, 269, 1824, 146, 1709, 3283, 270, 1855, 290, 1884, 145, 1748, 3370, 155, 1778, 3411, 277, 1908, 3547, 161, 1802, 3444, 286, 1932, 169, 1812, 3461, 288, 1949, 3607, 273, 1944, 3598, 284, 1965, 3644, 293, 1978, 3681, 294, 2000, 3691, 276, 1987, 3674, 297, 2004, 3717, 296, 2010, 3736, 317, 2044, 282, 2013, 3748, 306, 2057, 292, 2037, 3794, 307, 2068, 3842, 324, 2093, 3872, 285, 2080, 3879, 310, 2124, 331, 2152, 315, 2134, 312, 2141, 3948, 337, 2172, 4010, 316, 2169, 311, 2154, 3993, 328, 2185, 320, 2202, 308, 2203, 354, 2205, 322, 2196, 4089, 340, 2243, 4134, 325, 2222, 4128, 341, 2256, 4177, 318, 2241, 4168, 177, 2106, 4047, 332, 2269, 4208, 342, 2284, 183, 2128, 4082, 336, 2293, 4252, 349, 2310, 329, 2292, 4259, 338, 2304, 185, 2170, 4139, 376, 2358, 353, 2347, 4365, 187, 2208, 4239, 194, 2213, 4246, 344, 2382, 4423, 345, 2392, 350, 2399, 4444, 357, 2423, 206, 2268, 4339, 201, 2274, 4352, 366, 2464, 359, 2436, 205, 2300, 4403, 360, 2477, 351, 2473, 202, 2325, 4452, 389, 2527, 368, 2523, 356, 2503, 4652, 367, 2524, 4689, 370, 2543, 214, 2388, 4565, 378, 2560, 379, 2562, 363, 2557, 4752, 373, 2574, 4783, 384, 2613, 4828, 375, 2593, 4820, 385, 2619, 4865, 387, 2640, 4898, 396, 2659, 4916, 405, 2690, 388, 2679, 4984, 390, 2696, 5003, 410, 2725, 399, 2716, 397, 2718, 5077, 392, 2715, 380, 2707, 5060, 401, 2763, 400, 2774, 5160, 406, 2797, 5192, 414, 2816, 409, 2822, 5265, 412, 2861, 428, 2847, 418, 2871, 413, 2840, 5295, 209, 2670, 5132, 421, 2884, 5355, 440, 2909, 426, 2900, 5379, 424, 2905, 404, 2891, 5382, 213, 2708, 5205, 434, 2943, 398, 2896, 5409, 420, 2927, 5442, 425, 2944, 5477, 432, 2950, 217, 2775, 5312, 259, 2820, 215, 2769, 5328, 431, 2994, 423, 2989, 5556, 429, 3006, 219, 2788, 5370, 436, 3014, 5608, 395, 2982, 221, 2810, 5412, 433, 3032, 5635, 444, 3050, 435, 3049, 218, 2829, 5452, 498, 3125, 456, 3105, 463, 3092, 438, 3079, 5730, 443, 3096, 5797, 448, 3169, 464, 3186, 439, 3082, 5805, 460, 3203, 441, 3175, 5934, 449, 3220, 6018, 473, 3246, 6025, 476, 3285, 472, 3257, 6068, 459, 3282, 6097, 468, 3307, 480, 3321, 6175, 237, 3100, 5945, 483, 3342, 247, 3102, 5960, 487, 3354, 485, 3363, 450, 3316, 254, 3135, 6020, 249, 3150, 6043, 465, 3359, 6265, 488, 3390, 469, 3380, 274, 3192, 6121, 484, 3407, 474, 3405, 6340, 291, 3232, 6174, 475, 3422, 6373, 518, 3467, 262, 3221, 6183, 506, 3471, 490, 3456, 267, 3240, 6214, 491, 3468, 6451, 486, 3472, 477, 3464, 6462, 479, 3484, 6477, 508, 3515, 6544, 503, 3525, 494, 3529, 6556, 523, 3562, 509, 3552, 6599, 492, 3538, 6601, 516, 3573, 496, 3567, 6632, 513, 3604, 507, 3592, 6678, 512, 3605, 504, 3617, 6715, 522, 3621, 6724, 515, 3632, 525, 3643, 6770, 287, 3420, 6551, 520, 3659, 321, 3463, 6606, 524, 3671, 6820, 278, 3429, ...

And a graph showing the sequence SP (red) and the first differences (semi-primes in blue):

Best,

Alois

__________

Many thanks, Alois, nice job!

É.

__________