cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A364615 Numbers k such that the average of the decimal digits of 2^k is closer to 9/2 (the expected average for random digits) than for any smaller power of 2.

Original entry on oeis.org

0, 1, 2, 8, 14, 20, 29, 47, 62, 80, 113, 134, 182, 206, 281, 287, 299, 326, 419, 500, 560, 620, 638, 674, 833, 911, 1271, 1289, 1376, 1418, 1583, 1670, 1814, 2273, 2753, 3365, 3794, 4127, 4160, 4202, 4280, 4292, 4538, 4553, 4646, 4805, 4952, 4979, 5105, 5276
Offset: 1

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The average of the digits of 2^k is never exactly 9/2, because the sum of digits cannot be divisible by 3.
Conjecture: for each term k > 1, digitsum(2^k) - (9/2)*number_of_digits(2^k) = 1/2 if k is odd, -1/2 if k is even. - Jon E. Schoenfield, Jul 30 2023

Examples

			   k |   2^k | average of digits | distance from 9/2 | new minimum?
  ---+-------+-------------------+-------------------+-------------
   0 |     1 |         1         |        7/2        |     yes
   1 |     2 |         2         |        5/2        |     yes
   2 |     4 |         4         |        1/2        |     yes
   3 |     8 |         8         |        7/2        |
   4 |    16 |        7/2        |         1         |
   5 |    32 |        5/2        |         2         |
   6 |    64 |         5         |        1/2        |
   7 |   128 |       11/3        |        5/6        |
   8 |   256 |       13/3        |        1/6        |     yes
   9 |   512 |        8/3        |       11/6        |
  10 |  1024 |        7/4        |       11/4        |
  11 |  2048 |        7/2        |         1         |
  12 |  4096 |       19/4        |        1/4        |
  13 |  8192 |         5         |        1/2        |
  14 | 16384 |       22/5        |        1/10       |     yes
		

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