1,1

Since A110592 = "string-length of base 5 representation of n", we have A110592 = A110595 # 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(n) is the total number of holes in all nonnegative n-digit integers. For example, 0, 6 and 9 have 1 hole, while 8 has 2 holes. That adds up to a total of 5 for 1-digit integers. - Tanya Khovanova (tanyakh(AT)yahoo.com), Sep 18 2007

a(1) = 5, a(2) = 20, for n>2: a(n+1) = 5*a(n) = 4*(5^n) = 4*A000351. For n>2: a(n) = 100*(5^(n-1)) = 100*A000351(n-1). For n>1, cumulative sum of a(n) = A000351(n) = powers of 5. a(n) = the number of occurrences of the integer n in A110592 = "string-length of base 5 representation of n" = the number of occurrences of the integer n in "string-length of A007091."

O.g.f.: 5x(1-x)/(1-5x). - Better definition from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2008

Cf. A000351, A007091, A081604, A110591, A110592, A110593, A110594.

Sequence in context: A020046 A026118 A108509 this_sequence A092640 A109500 A137961

Adjacent sequences: A110592 A110593 A110594 this_sequence A110596 A110597 A110598

easy,nonn

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

Better definition from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2008