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%I A337225 #13 Aug 22 2020 18:51:15
%S A337225 1,1,1,2,2,1,2,3,3,2,2,2,4,2,3,4,4,3,3,4,4,2,3,3,6,4,4,4,6,3,4,5,5,4,
%T A337225 4,6,6,4,5,6,6,4,3,4,6,3,4,4,8,6,6,8,8,4,6,6,9,6,6,6,8,4,5,6,6,5,5,8,
%U A337225 8,6,7,9,9,6,5,8,10,6,7,8,8,6,5,8,6,3,5
%N A337225 a(n) is the number of distinct integers k that can be obtained by starting from the binary expansion of n and repeatedly replacing some square XX by X.
%C A337225 Leading zeros in binary expansions are ignored.
%C A337225 The least possible k is:
%C A337225 - 0 for n = 0,
%C A337225 - 1 for n = 2^m-1 for some m > 0,
%C A337225 - 2 for n = 2*m for some m > 0,
%C A337225 - 5 otherwise.
%H A337225 Rémy Sigrist, Table of n, a(n) for n = 0..8192
%H A337225 Rémy Sigrist, PARI program for A337225
%H A337225 Index entries for sequences related to binary expansion of n
%F A337225 a(2^k-1) = k for any k > 0.
%e A337225 The first terms, alongside the binary expansions of n and of the corresponding k's, are:
%e A337225 n a(n) bin(n) {bin(k)}
%e A337225 -- ---- ------ -------------------
%e A337225 0 1 0 {0}
%e A337225 1 1 1 {1}
%e A337225 2 1 10 {10}
%e A337225 3 2 11 {1, 11}
%e A337225 4 2 100 {10, 100}
%e A337225 5 1 101 {101}
%e A337225 6 2 110 {10, 110}
%e A337225 7 3 111 {1, 11, 111}
%e A337225 8 3 1000 {10, 100, 1000}
%e A337225 9 2 1001 {101, 1001}
%e A337225 10 2 1010 {10, 1010}
%e A337225 11 2 1011 {101, 1011}
%e A337225 12 4 1100 {10, 100, 110, 1100}
%e A337225 13 2 1101 {101, 1101}
%e A337225 14 3 1110 {10, 110, 1110}
%e A337225 15 4 1111 {1, 11, 111, 1111}
%e A337225 16 4 10000 {10, 100, 1000, 10000}
%o A337225 (PARI) See Links section.
%Y A337225 Cf. A337222.
%K A337225 nonn,base
%O A337225 0,4
%A A337225 _Rémy Sigrist_, Aug 19 2020
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