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 A186775 #20 Oct 01 2022 01:13:35
%S A186775 3,4,8,9,15,16,20,21,23,24,26,28,29,33,34,36,39,40,41,46,48,51,52,55,
%T A186775 56,57,60,63,64,67,68,69,74,75,76,77,80,82,83,85,86,88,91,92,94,95,97,
%U A186775 98,100,102,106,108,112,113,116,118,121,124,126
%N A186775 Numbers k such that digitsum(2^k) > digitsum(2^(k+1)).
%C A186775 If 2^k and 2^(k+1) acted like random numbers of their size, the probability that k would be in the sequence would be 1/2 + O(1/k). So very possibly a(n) ~ 2n. - _Charles R Greathouse IV_, Aug 08 2022
%H A186775 J.W.L. (Jan) Eerland, <a href="/A186775/b186775.txt">Table of n, a(n) for n = 1..49688</a>
%e A186775 3 is in the sequence because digitsum(2^3) = 8 > 7 = digitsum(2^4).
%t A186775 DeleteCases[Table[If[Total[Total[IntegerDigits[2^n]]]>Total[IntegerDigits[2^(n+1)]],n,k],{n,0, 10^5}],k] (* _J.W.L. (Jan) Eerland_, Aug 08 2022 *)
%o A186775 (Sage) def is_A186775(n): return sum((2^n).digits()) > sum((2^(n+1)).digits()) # _D. S. McNeil_, Feb 27 2011
%o A186775 (Python)
%o A186775 from itertools import count, islice, pairwise
%o A186775 def ds2(n): return sum(map(int, str(1<<n)))
%o A186775 def agen(): yield from (k for k, t in enumerate(pairwise(map(ds2, count(1))), 1) if t[0] > t[1])
%o A186775 print(list(islice(agen(), 60))) # _Michael S. Branicky_, Aug 08 2022
%Y A186775 Cf. A001370.
%K A186775 base,easy,nonn
%O A186775 1,1
%A A186775 _Thomas Nordhaus_, Feb 26 2011