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Indices of records in A159918.
9

%I #48 Nov 30 2022 10:27:45

%S 0,1,3,5,11,21,39,45,75,155,181,627,923,1241,2505,3915,5221,6475,

%T 11309,15595,19637,31595,44491,69451,113447,185269,244661,357081,

%U 453677,908091,980853,2960011,2965685,5931189,11862197,20437147,22193965,43586515,57804981,157355851

%N Indices of records in A159918.

%C 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 Lindström mentions that the record value 34 in A159918 is first reached at n = 980853.

%H 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 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 Lindström shows that lim sup wt(m^2)/log_2 m = 2.

%o (Haskell)

%o a230097 n = a230097_list !! (n-1)

%o a230097_list = 0 : f 0 0 where

%o f i m = if v > m then i : f (i + 1) v else f (i + 1) m

%o where v = a159918 i

%o -- _Reinhard Zumkeller_, Oct 12 2013

%o (Python 3.10+)

%o from itertools import count, islice

%o def A230097_gen(): # generator of terms

%o c = -1

%o for n in count(0):

%o if (m := (n**2).bit_count())>c:

%o yield n

%o c = m

%o A230097_list = list(islice(A230097_gen(),20)) # _Chai Wah Wu_, Oct 01 2022

%Y Cf. A000120, A159918, A231897, A357304, A357658.

%K nonn,base

%O 1,3

%A _N. J. A. Sloane_, Oct 11 2013

%E a(19)-a(40) from _Reinhard Zumkeller_, Oct 12 2013