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A230097 Indices of records in A159918.

%I A230097 #48 Nov 30 2022 10:27:45
%S A230097 0,1,3,5,11,21,39,45,75,155,181,627,923,1241,2505,3915,5221,6475,
%T A230097 11309,15595,19637,31595,44491,69451,113447,185269,244661,357081,
%U A230097 453677,908091,980853,2960011,2965685,5931189,11862197,20437147,22193965,43586515,57804981,157355851
%N A230097 Indices of records in A159918.
%C A230097 The records themselves are not so interesting: 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, ... (A357304).
%C A230097 Lindström mentions that the record value 34 in A159918 is first reached at n = 980853.
%H A230097 Bert Dobbelaere, <a href="/A230097/b230097.txt">Table of n, a(n) for n = 1..80</a>, (terms 41..64 from Donovan Johnson, 65..70 from Hugo Pfoertner, missing 68 and 72..80 from Bert Dobbelaere).
%H A230097 Bernt Lindström, <a href="http://dx.doi.org/10.1006/jnth.1997.2129">On the binary digits of a power</a>, Journal of Number Theory, Volume 65, Issue 2, August 1997, Pages 321-324.
%F A230097 Lindström shows that lim sup wt(m^2)/log_2 m = 2.
%o A230097 (Haskell)
%o A230097 a230097 n = a230097_list !! (n-1)
%o A230097 a230097_list = 0 : f 0 0 where
%o A230097    f i m = if v > m then i : f (i + 1) v else f (i + 1) m
%o A230097            where v = a159918 i
%o A230097 -- _Reinhard Zumkeller_, Oct 12 2013
%o A230097 (Python 3.10+)
%o A230097 from itertools import count, islice
%o A230097 def A230097_gen(): # generator of terms
%o A230097     c = -1
%o A230097     for n in count(0):
%o A230097         if (m := (n**2).bit_count())>c:
%o A230097             yield n
%o A230097             c = m
%o A230097 A230097_list = list(islice(A230097_gen(),20)) # _Chai Wah Wu_, Oct 01 2022
%Y A230097 Cf. A000120, A159918, A231897, A357304, A357658.
%K A230097 nonn,base
%O A230097 1,3
%A A230097 _N. J. A. Sloane_, Oct 11 2013
%E A230097 a(19)-a(40) from _Reinhard Zumkeller_, Oct 12 2013