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How many of the 343 smallest positive integers written in base 7 use 0 or 1 (or both) as a digit?

 Jan 29, 2022
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These are the first 343 integers in base 7. Just count the ones with a "zero" or/and a "1" in them:

 

(1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 66, 100, 101, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 115, 116, 120, 121, 122, 123, 124, 125, 126, 130, 131, 132, 133, 134, 135, 136, 140, 141, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 166, 200, 201, 202, 203, 204, 205, 206, 210, 211, 212, 213, 214, 215, 216, 220, 221, 222, 223, 224, 225, 226, 230, 231, 232, 233, 234, 235, 236, 240, 241, 242, 243, 244, 245, 246, 250, 251, 252, 253, 254, 255, 256, 260, 261, 262, 263, 264, 265, 266, 300, 301, 302, 303, 304, 305, 306, 310, 311, 312, 313, 314, 315, 316, 320, 321, 322, 323, 324, 325, 326, 330, 331, 332, 333, 334, 335, 336, 340, 341, 342, 343)

 Jan 29, 2022

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