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https://www.psychforums.com/blog/highdimensionman/the_number_pi_in_a_factorial_base._b-10857_sid-a04f66af7b1a722b1757c21a5e728531.html
Author:  highdimensionman [ Thu Mar 09, 2017 8:26 am ]
Blog Subject:  The number Pi in a Factorial Base.
In a standard Factorial base the end digit is a 1 or 0 then the next digit along is a 0,1 or 2 and the digit after that is 0,1,2 or 3 ect ect and so on. I've done a bit of figuring out and decided to show you peps what Pi looks like in this Base. Notice where you find square and cubic numbers is almost regular could this be telling us something deep about numbers It also seems as if every possible number comes up in this sequence such would be an interesting thing to try and prove and disprove.

Heres the first 1002 digits of this number represented in base 10...

{1, 1}
.
{0, 0, 3, 1, 5, 6, 5, 0, 1, 4, 7, 8, 0, 6, 7, 10, 7, 10, 4,
10, 6, 16, 1, 11, 20, 3, 18, 12, 9, 13, 18, 21, 14, 34, 27, 11, 27,
33, 36, 18, 5, 18, 5, 23, 39, 1, 10, 42, 28, 17, 20, 51, 8, 42, 47,
0, 27, 23, 16, 52, 32, 52, 53, 24, 43, 61, 64, 18, 17, 11, 0, 53,
14, 62, 0, 38, 26, 27, 23, 18, 13, 66, 47, 83, 78, 23, 37, 73, 37,
41, 35, 68, 63, 15, 23, 36, 90, 26, 47, 73, 32, 55, 22, 97, 103, 50,
83, 29, 62, 92, 44, 29, 105, 67, 24, 94, 77, 36, 48, 29, 64, 26,
93, 71, 111, 80, 126, 125, 65, 49, 98, 43, 66, 13, 28, 4, 94, 113,
86, 15, 113, 39, 44, 71, 22, 22, 136, 16, 134, 131, 86, 61, 92, 75,
20, 86, 103, 20, 43, 81, 5, 81, 163, 131, 130, 159, 105, 110, 61,
140, 19, 142, 136, 123, 105, 86, 7, 107, 4, 176, 43, 61, 137, 69,
37, 144, 107, 136, 2, 181, 19, 12, 48, 143, 151, 22, 4, 128, 85,
145, 195, 90, 159, 6, 120, 102, 57, 100, 112, 62, 208, 78, 19, 57,
157, 192, 148, 38, 14, 47, 104, 215, 210, 72, 26, 3, 6, 175, 229,
74, 161, 81, 174, 115, 28, 127, 183, 127, 87, 80, 52, 136, 140, 199,
198, 183, 21, 74, 75, 212, 157, 152, 109, 21, 93, 94, 143, 244, 37,
230, 218, 88, 71, 52, 160, 183, 77, 256, 140, 83, 95, 102, 101,
175, 268, 124, 242, 237, 252, 205, 67, 200, 229, 250, 26, 159, 82,
259, 262, 123, 188, 206, 80, 148, 235, 272, 109, 105, 97, 245, 22,
170, 127, 181, 200, 289, 278, 30, 218, 217, 48, 209, 28, 118, 143,
53, 297, 30, 184, 276, 55, 34, 296, 134, 116, 132, 10, 252, 111,
234, 34, 219, 235, 17, 21, 158, 257, 217, 253, 209, 242, 212, 334,
103, 3, 314, 233, 178, 119, 272, 26, 227, 189, 132, 129, 185, 282,
77, 256, 27, 95, 281, 109, 152, 26, 154, 156, 195, 168, 35, 4, 266,
50, 319, 79, 349, 325, 324, 296, 211, 153, 129, 158, 128, 312, 209,
213, 322, 380, 361, 11, 338, 364, 189, 1, 381, 222, 385, 211, 155,
138, 165, 104, 118, 265, 173, 366, 214, 69, 59, 147, 327, 171, 47,
115, 204, 280, 289, 360, 91, 80, 117, 44, 223, 255, 64, 336, 311,
314, 293, 207, 395, 104, 286, 39, 183, 168, 285, 273, 280, 79, 333,
44, 426, 40, 270, 18, 305, 18, 168, 348, 415, 400, 136, 448, 270,
121, 407, 215, 259, 421, 433, 441, 8, 289, 421, 341, 307, 248, 164,
407, 173, 193, 381, 382, 410, 418, 178, 431, 397, 306, 446, 362,
260, 8, 79, 208, 168, 440, 323, 327, 24, 428, 391, 104, 12, 166, 4,
436, 436, 395, 168, 497, 166, 128, 74, 285, 287, 3, 341, 483, 228,
131, 24, 56, 144, 139, 43, 230, 313, 80, 318, 174, 16, 15, 27, 349,
446, 117, 297, 28, 249, 97, 431, 134, 102, 430, 370, 92, 281, 38,
226, 239, 427, 12, 214, 482, 516, 201, 39, 535, 0, 14, 279, 322,
160, 63, 503, 149, 480, 153, 206, 260, 302, 167, 146, 139, 365, 489,
557, 40, 331, 43, 328, 394, 32, 77, 342, 382, 385, 242, 123, 367,
507, 572, 369, 531, 112, 471, 2, 429, 381, 407, 324, 437, 542, 53,
37, 272, 205, 509, 285, 36, 110, 174, 118, 212, 315, 429, 188, 233,
592, 16, 435, 492, 163, 328, 142, 64, 583, 96, 371, 70, 404, 55, 34,
409, 114, 577, 612, 376, 406, 266, 212, 619, 569, 627, 95, 70, 420,
166, 34, 623, 147, 49, 398, 576, 370, 16, 405, 86, 191, 115, 54,
302, 128, 641, 414, 506, 636, 617, 206, 455, 68, 338, 89, 398, 273,
258, 211, 370, 590, 504, 213, 403, 322, 441, 196, 330, 151, 44, 506,
180, 395, 583, 331, 236, 610, 154, 673, 403, 95, 326, 443, 399,
173, 355, 223, 503, 391, 47, 442, 214, 315, 303, 187, 59, 99, 703,
141, 499, 700, 507, 570, 235, 438, 372, 688, 442, 636, 151, 269,
276, 687, 183, 719, 559, 354, 590, 118, 398, 714, 78, 218, 175, 116,
656, 147, 631, 314, 493, 88, 178, 221, 239, 19, 73, 84, 245, 578,
299, 64, 713, 125, 339, 624, 679, 92, 475, 136, 50, 11, 237, 463,
587, 408, 373, 396, 450, 674, 65, 557, 49, 508, 384, 463, 740, 613,
649, 135, 233, 622, 455, 390, 8, 179, 679, 158, 240, 687, 692, 758,
336, 412, 63, 5, 566, 370, 703, 701, 53, 542, 727, 372, 288, 798,
113, 545, 54, 238, 453, 348, 615, 135, 465, 136, 656, 596, 355, 1,
362, 119, 368, 78, 396, 592, 525, 479, 646, 540, 295, 409, 458, 765,
383, 266, 416, 469, 31, 510, 473, 590, 494, 831, 551, 462, 620,
556, 443, 548, 658, 316, 815, 420, 704, 580, 434, 794, 127, 479,
783, 675, 586, 225, 210, 103, 580, 257, 716, 595, 241, 77, 381, 795,
480, 382, 541, 376, 100, 347, 395, 144, 600, 473, 129, 345, 553,
223, 143, 564, 678, 229, 730, 865, 441, 655, 422, 696, 7, 694, 679,
352, 756, 263, 444, 620, 754, 41, 154, 225, 186, 395, 481, 761, 190,
386, 608, 154, 383, 31, 63, 879, 244, 763, 453, 733, 51, 105, 835,
381, 45, 866, 404, 863, 718, 267, 506, 907, 451, 246, 470, 226, 111,
441, 393, 418, 374, 17, 942, 891, 376, 283, 521, 119, 675, 205, 41,
194, 19, 354, 92, 737, 722, 95, 141, 704, 650, 266, 329, 399, 534,
651, 532, 896, 929, 516, 230, 324, 627, 911, 552, 487, 469, 364,
702, 818, 875, 719, 194, 63, 449, 502, 146, 42, 254, 263, 617, 821}
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