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}