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A230419 Square array A(n,k) = difference of digit sums in factorial base representations (A007623) of n and k, n>=0, k>=0, read by antidiagonals; A(n,k) = A034968(n)-A034968(k). 3
0, 1, -1, 1, 0, -1, 2, 0, 0, -2, 2, 1, 0, -1, -2, 3, 1, 1, -1, -1, -3, 1, 2, 1, 0, -1, -2, -1, 2, 0, 2, 0, 0, -2, 0, -2, 2, 1, 0, 1, 0, -1, 0, -1, -2, 3, 1, 1, -1, 1, -1, 1, -1, -1, -3, 3, 2, 1, 0, -1, 0, 1, 0, -1, -2, -3, 4, 2, 2, 0, 0, -2, 2, 0, 0, -2, -2, -4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
Equivalently, A(n,k) = the sum of differences of digits in matching positions of the factorial base representations (A007623) of n and k.
LINKS
FORMULA
A(col,row) = A034968(col)-A034968(row). [Where col is the column and row the row index of entry A(col,row)]
Equally, as a sequence, a(n) = A034968(A025581(n)) - A034968(A002262(n)).
For each entry, A(j,i) = -A(i,j), or as a sequence, a(A061579(n)) = -a(n). [The array is symmetric up to the sign of entries]
Also, for each entry A(i,j), abs(A(i,j)) <= A231713(i,j).
EXAMPLE
The top left corner array is:
0, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, ...
-1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, ...
-1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, ...
-2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ...
-2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ...
-3, -2, -2, -1, -1, 0, -2, -1, -1, 0, 0, ...
-1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, ...
-2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ...
-2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ...
-3, -2, -2, -1, -1, 0, -2, -1, -1, 0, 0, ...
-3, -2, -2, -1, -1, 0, -2, -1, -1, 0, 0, ...
...
PROG
(Scheme, two alternative versions)
(define (A230419 n) (- (A034968 (A025581 n)) (A034968 (A002262 n))))
;; A "stand-alone" version:
(define (A230419 n) (A230419bi (A025581 n) (A002262 n)))
(define (A230419bi 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 (- (modulo x i) (modulo y i))))))))
CROSSREFS
The topmost row: A034968 (and also the leftmost column negated).
Cf. A230415 (similar array which gives the number of differing digits).
Cf. A231713 (similar array which gives the sum of absolute differences).
Sequence in context: A329767 A356018 A107502 * A146165 A308831 A277327
KEYWORD
sign,base,tabl
AUTHOR
Antti Karttunen, Nov 10 2013
STATUS
approved

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Last modified July 13 00:23 EDT 2024. Contains 374259 sequences. (Running on oeis4.)