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A053087 a(n) is the smallest j for which 2^j kara n is defined (see A053405).

%I A053087 #14 Feb 03 2023 01:35:11
%S A053087 0,1,3,2,5,4,5,3,7,6,5,7,6,8,7,4,9,8,7,8,9,6,9,8,9,7,9,10,8,10,9,5,11,
%T A053087 10,9,10,8,10,11,9,10,11,7,11,10,11,9,11,10,11,12,8,11,10,12,11,9,12,
%U A053087 11,12,10,12,11,6,13,12,11,12,10,12,11,12,13,9,12,11,13,12,10
%N A053087 a(n) is the smallest j for which 2^j kara n is defined (see A053405).
%H A053087 Reinhard Zumkeller, <a href="/A053087/b053087.txt">Table of n, a(n) for n = 1..1000</a>
%e A053087 a(6)=4 because 2^3 kara 6 is undefined, but 16 kara 6 = 3.
%o A053087 (Haskell)
%o A053087 a053087 n = head [j | j <- [0..], (2 ^ j) `kara` n /= Nothing] where
%o A053087    kara a b = if null ks then Nothing else Just $ head ks
%o A053087               where ks = [c | c <- [1..a], a <= c * b, a > c * (b - 1)]
%o A053087 -- _Reinhard Zumkeller_, Mar 30 2013
%Y A053087 Cf. A053405.
%Y A053087 A053092(n) = 2^a(n) kara n.
%K A053087 nonn,look
%O A053087 1,3
%A A053087 Robert Lozyniak (11(AT)onna.com), Feb 26 2000
%E A053087 More terms from Antony M. Goddard, cat(AT)animal.u-net.com or tony(AT)noggin.lowtech.org, Oct 13 2000