A231714 Lower triangular region of A231713; A triangular table read by rows: T(n,k) = sum of absolute values of digit differences in the factorial base representations (A007623) of n and k, where (n, k) = (0,0), (1,0), (1,1), (2,0), (2,1), (2,2), ..., n >= 0 and (0 <= k <= n).

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

Offset: 0

Author

Antti Karttunen, Nov 12 2013

Keywords

• nonn
• base
• tabl

Examples

			This triangular table begins as:
  0;
  1, 0;
  1, 2, 0;
  2, 1, 1, 0;
  2, 3, 1, 2, 0;
  3, 2, 2, 1, 1, 0;
  1, 2, 2, 3, 3, 4, 0;
  2, 1, 3, 2, 4, 3, 1, 0;
  ...
Please see A231713 for examples how the terms are computed.
		

Links

• Antti Karttunen, Rows n = 0..120 of triangle, flattened

Crossrefs

The leftmost column: A034968.

This is a lower, or equivalently, an upper triangular subregion of symmetric square array A231713. Cf. A230417.

Programs

Scheme

(define (A231714 n) (A231713bi (A003056 n) (A002262 n)))
(define (A231713bi x y) (let loop ((x x) (y y) (i 2) (d 0)) (cond ((and (zero? x) (zero? y)) d) (else (loop (floor->exact (/ x i)) (floor->exact (/ y i)) (+ i 1) (+ d (abs (- (modulo x i) (modulo y i)))))))))

Formula

a(n) = A231713(A003056(n),A002262(n)). [As a sequence, this is obtained by taking a subsection from array A231713.]

T(n,0) = A034968(n). [The leftmost column]

Each entry T(n,k) >= A230417(n,k).