1,1

a(n) is the index of zeros in the complement of the square analogue of the Baum-Sweet sequence, which is b(n) = 1 if the binary representation of n contains no block of consecutive zeros of exactly a nontrivial square number length; otherwise b(n) = 0.

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 157.

J.-P. Allouche, Finite Automata and Arithmetic.

a(n) is in this sequence iff n (base 2) has a block (not a sub-block) of k^2 = A000290(k) consecutive zeros for k>1.

a(1) = 16 because 16 (base 2) = 10000, which has a block of 4 = 2^2 zeros.

a(2) = 33 because 33 (base 2) = 100001, which has a block of 4 zeros.

a(3) = 48 because 48 (base 2) = 110000, which has a block of 4 zeros.

a(49) = 512 because 512 (base 2) = 1000000000, with a block of 9 = 3^2 zeros.

Similarly, there are blocks of exactly 9 zeros in 1025, 1536, 2050, 2051, 3073, 3584, 7149, 8196, 8197, 8198, 8199.

65536, 131073, 196608, 262146 and 262147 are in this sequence because (base 2) they each have a block of 16 = 4^2 zeros.

33554432 has a block of 25 = 5^2 zeros.

Select[Range[531], Or @@ (First[ # ] == 0 && Length[ # ] > 1 && IntegerQ[Length[ # ]^(1/2)] &) /@ Split[IntegerDigits[ #, 2]] &] (*Chandler*)

Cf. A000290, A037011, A086747, A110471, A110472, A110474.

Sequence in context: A070591 A151981 A110472 this_sequence A095784 A041502 A041500

Adjacent sequences: A110499 A110500 A110501 this_sequence A110503 A110504 A110505

base,easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 11 2005

Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 12 2005