A230097 Indices of records in A159918.

0, 1, 3, 5, 11, 21, 39, 45, 75, 155, 181, 627, 923, 1241, 2505, 3915, 5221, 6475, 11309, 15595, 19637, 31595, 44491, 69451, 113447, 185269, 244661, 357081, 453677, 908091, 980853, 2960011, 2965685, 5931189, 11862197, 20437147, 22193965, 43586515, 57804981, 157355851

Offset

1,3

Comments

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).

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

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..80, (terms 41..64 from Donovan Johnson, 65..70 from Hugo Pfoertner, missing 68 and 72..80 from Bert Dobbelaere).

Bernt Lindström, On the binary digits of a power, Journal of Number Theory, Volume 65, Issue 2, August 1997, Pages 321-324.

Formula

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

Prog

(Haskell)
a230097 n = a230097_list !! (n-1)
a230097_list = 0 : f 0 0 where
   f i m = if v > m then i : f (i + 1) v else f (i + 1) m
           where v = a159918 i
-- Reinhard Zumkeller, Oct 12 2013
(Python 3.10+)
from itertools import count, islice
def A230097_gen(): # generator of terms
    c = -1
    for n in count(0):
        if (m := (n**2).bit_count())>c:
            yield n
            c = m
A230097_list = list(islice(A230097_gen(), 20)) # Chai Wah Wu, Oct 01 2022

Crossrefs

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

Sequence in context: A045515 A298342 A293317 * A146787 A147243 A372451

Adjacent sequences: A230094 A230095 A230096 * A230098 A230099 A230100

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 11 2013

Extensions

a(19)-a(40) from Reinhard Zumkeller, Oct 12 2013

Status

approved