A295896 - OEIS

A295896

a(n) = 1 if there are no odd runs of 1's in the binary expansion of n followed by a 0 to their right, 0 otherwise.

1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1

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OFFSET

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

Index entries for characteristic functions

FORMULA

a(0) = 1; and then after, for odd n, a(n) = a((n-1)/2), for even n, a(n) = 0 if A007814(1+(n/2)) is odd, otherwise a(n/2).

a(n) = A053866(A005940(1+n)) = A000035(A000203(A005940(1+n))).

a(n) = A295875(n) + A295895(n) mod 2.

EXAMPLE

Drawing the terms as a binary tree (the first six levels shown) helps in seeing where terms of A028982 (squares and twice squares) are located in Doudna-tree (A005940, at the positions where 1's occur here):

............../ \..............

0 1

....../ \...... ....../ \......

0 0 1 1

/ \ / \ / \ / \

0 0 0 0 1 1 0 1

/ \ / \ / \ / \ / \ / \ / \ / \

0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1

MATHEMATICA

Array[Boole@ NoneTrue[Partition[PadRight[#, # + Boole[OddQ@ #] &@ Length@ #, ""] /. _?StringQ -> {0, 0}, 2, 2][[All, All, -1]] &@ Map[{First@ #, Length@ #} &, Split@ IntegerDigits[#, 2]], And[OddQ@ #1, #2 > 0] & @@ # &] &, 120, 0] (* Michael De Vlieger, Dec 02 2017 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A295896 n) (cond ((zero? n) 1) ((odd? n) (A295896 (/ (- n 1) 2))) ((odd? (A007814 (+ 1 (/ n 2)))) 0) (else (A295896 (/ n 2)))))

CROSSREFS

Cf. A005940, A007814, A037011, A053866, A295875, A295895.

Characteristic function of A295897.

Sequence in context: A189920 A318963 A350600 * A176918 A176890 A164057

Adjacent sequences: A295893 A295894 A295895 * A295897 A295898 A295899

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Dec 01 2017

STATUS

approved