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.
%I A364615 #7 Aug 02 2023 13:46:22 %S A364615 0,1,2,8,14,20,29,47,62,80,113,134,182,206,281,287,299,326,419,500, %T A364615 560,620,638,674,833,911,1271,1289,1376,1418,1583,1670,1814,2273,2753, %U A364615 3365,3794,4127,4160,4202,4280,4292,4538,4553,4646,4805,4952,4979,5105,5276 %N 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. %C A364615 The average of the digits of 2^k is never exactly 9/2, because the sum of digits cannot be divisible by 3. %C A364615 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 %e A364615 k | 2^k | average of digits | distance from 9/2 | new minimum? %e A364615 ---+-------+-------------------+-------------------+------------- %e A364615 0 | 1 | 1 | 7/2 | yes %e A364615 1 | 2 | 2 | 5/2 | yes %e A364615 2 | 4 | 4 | 1/2 | yes %e A364615 3 | 8 | 8 | 7/2 | %e A364615 4 | 16 | 7/2 | 1 | %e A364615 5 | 32 | 5/2 | 2 | %e A364615 6 | 64 | 5 | 1/2 | %e A364615 7 | 128 | 11/3 | 5/6 | %e A364615 8 | 256 | 13/3 | 1/6 | yes %e A364615 9 | 512 | 8/3 | 11/6 | %e A364615 10 | 1024 | 7/4 | 11/4 | %e A364615 11 | 2048 | 7/2 | 1 | %e A364615 12 | 4096 | 19/4 | 1/4 | %e A364615 13 | 8192 | 5 | 1/2 | %e A364615 14 | 16384 | 22/5 | 1/10 | yes %Y A364615 Cf. A000079, A001370, A034887, A364606. %K A364615 nonn,base %O A364615 1,3 %A A364615 _Pontus von Brömssen_ and _Jon E. Schoenfield_, Jul 29 2023