1,1

Since A110591 = "string-length of base 4 representation of n", we have A110591 = A110594 # n. This is in terms of the repetition convolution operator #, where (sequence A) # (sequence B) = the sequence consisting of A(n) copies of B(n). Over the set of positive infinite integer sequences, # gives a nonassociative noncommutative groupoid (magma) with a left identity (A000012) but no right identity, where the left identity is also a right nullifier, and idempotent. For any positive integer constant c, the sequence c*A000012 = (c,c,c,c,...) is also a right nullifier; for c = 1, this is A000012; for c = 3 this is A010701.

a(1) = 4, a(2) = 12, for n>2: a(n+1) = 4*a(n). For n>1, cumulative sum of a(n) = A000302(n) = powers of 4. a(n) = the number of occurrences of the integer n in A110591 = "string-length of base 4 representation of n" = the number of occurrences of the integer n in "string-length of A007090."

Cf. A000302, A007090, A081604, A110591, A110593.

Sequence in context: A019309 A056632 A092898 this_sequence A111930 A013935 A104708

Adjacent sequences: A110591 A110592 A110593 this_sequence A110595 A110596 A110597

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 29 2005