This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A230419 #13 Nov 17 2013 17:36:48 %S A230419 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, %T A230419 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, %U A230419 0,-1,0,1,0,-1,-2,-3,4,2,2,0,0,-2,2,0,0,-2,-2,-4 %N 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). %C A230419 Equivalently, A(n,k) = the sum of differences of digits in matching positions of the factorial base representations (A007623) of n and k. %H A230419 Antti Karttunen, <a href="/A230419/b230419.txt">The first 121 antidiagonals of the table, flattened</a> %F A230419 A(col,row) = A034968(col)-A034968(row). [Where col is the column and row the row index of entry A(col,row)] %F A230419 Equally, as a sequence, a(n) = A034968(A025581(n)) - A034968(A002262(n)). %F A230419 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] %F A230419 Also, for each entry A(i,j), abs(A(i,j)) <= A231713(i,j). %e A230419 The top left corner array is: %e A230419 0, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, ... %e A230419 -1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, ... %e A230419 -1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, ... %e A230419 -2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ... %e A230419 -2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ... %e A230419 -3, -2, -2, -1, -1, 0, -2, -1, -1, 0, 0, ... %e A230419 -1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, ... %e A230419 -2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ... %e A230419 -2, -1, -1, 0, 0, 1, -1, 0, 0, 1, 1, ... %e A230419 -3, -2, -2, -1, -1, 0, -2, -1, -1, 0, 0, ... %e A230419 -3, -2, -2, -1, -1, 0, -2, -1, -1, 0, 0, ... %e A230419 ... %o A230419 (Scheme, two alternative versions) %o A230419 (define (A230419 n) (- (A034968 (A025581 n)) (A034968 (A002262 n)))) %o A230419 ;; A "stand-alone" version: %o A230419 (define (A230419 n) (A230419bi (A025581 n) (A002262 n))) %o A230419 (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)))))))) %Y A230419 The topmost row: A034968 (and also the leftmost column negated). %Y A230419 Cf. A230415 (similar array which gives the number of differing digits). %Y A230419 Cf. A231713 (similar array which gives the sum of absolute differences). %K A230419 sign,base,tabl %O A230419 0,7 %A A230419 _Antti Karttunen_, Nov 10 2013