A244231 Maximum "digit" value in Semigreedy Catalan Representation of n, A244159.

0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 4, 3, 2, 2, 2, 2, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 4, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 4, 3, 3, 3, 3, 4, 4, 4, 5, 4, 3, 3, 3, 3, 4, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 4, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 1

Offset: 0

Author

Antti Karttunen, Jun 25 2014

Keywords

• nonn

Comments

The first value larger than nine occurs at a(33604) = 10. (33604 = A014143(9)). Note that this sequence is not subject to any corruption by decimal representation as A244159 itself is.

A014143 gives records up to that A014143(9) = 33604, but thereafter, the next record occurs at 57317, for which a(57317) = 11, although A014143(10) = 116103. This is explained by that A244159raw(57317) = [2,3,4,5,6,7,8,9,10,11] and A244159raw(116103) = [1,2,3,4,5,6,7,8,9,10,11] (where A244159raw means the underlying representation, before it is maimed by the decimal representation).

This change is explained by the fact that A014143(n-1) + A014138(n) > A000108(n+1) for n = 1..9, but for n >= 10, A014143(n-1) + A014138(n) < A000108(n+1).

For example, although 16808 = 2*C(9) + 3*C(8) + 4*C(7) + 5*C(6) + 6*C(5) + 7*C(4) + 8*C(3) + 9*C(2) + 10*C(1), its representation in A244159 system is 1000000123, as 16808 = 1*C(10) + 1*C(3) + 2*C(2) + 3*C(1).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..58786

Crossrefs

Cf. A244159, A244232, A014420, A197433, A244316.

Programs

Scheme

(define (A244231 n) (if (zero? n) 0 (apply max (vector->list (A244159raw n))))) ;; Code for A244159raw given in A244159.

Formula

For all n, a(A000108(n)) = 1.

For all n >= 1, a(A014138(n)) = 1.

For all n, a(A014143(n)) = n+1.