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 A085219 Array A(x,y): "rised concatenation" of factorial expansions of x & y, listed antidiagonalwise as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ... Zero is expanded as an empty string. 4
 0, 1, 1, 2, 5, 2, 3, 15, 14, 3, 4, 17, 56, 15, 4, 5, 21, 62, 57, 22, 5, 6, 23, 80, 63, 88, 23, 6, 7, 57, 86, 81, 94, 89, 54, 7, 8, 59, 272, 87, 112, 95, 270, 55, 8, 9, 63, 278, 273, 118, 113, 294, 271, 56, 9, 10, 65, 296, 279, 424, 119, 390, 295, 272, 57, 10, 11, 69, 302, 297, 430 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This is otherwise like A085215, except that to each digit in the factorial expansion of 'x' is added the most significant digit in the factorial expansion of 'y'. LINKS EXAMPLE To get A(4,3) = 81 we take the factorial expansions of 4 (= '20') and 3 (= '11') and then we add 1 to each digit of the former to get '31', before concatenating them as '3111' (3*24+1*6+1*2+1*1 = 81). Similarly, for A(3,4) = 94 we add 2 to 3's expansion '11' to get '33' and then the concatenation yields '3320' (3*24+3*6+2*2=94). See A085221 for the corresponding factorial expansions. PROG (MIT Scheme) (define (A085219bi x y) (let loop ((x x) (y y) (i 2) (j (1+ (A084558 y))) (r (car (n->factbase y)))) (cond ((zero? x) y) (else (loop (floor->exact (/ x i)) (+ (* (A000142 j) (+ r (modulo x i))) y) (1+ i) (1+ j) r))))) (define (n->factbase n) (let loop ((n n) (fex (if (zero? n) (list 0) (list))) (i 2)) (cond ((zero? n) fex) (else (loop (floor->exact (/ n i)) (cons (modulo n i) fex) (1+ i)))))) (define (A085219 n) (A085219bi (A025581 n) (A002262 n))) (define (A085220 n) (A085219bi (A002262 n) (A025581 n))) CROSSREFS Transpose: A085220. Can be used to compute A085203. Cf. A000142, A007623, A084558, A025581, A002262. Sequence in context: A197782 A197613 A085220 * A197207 A197805 A334754 Adjacent sequences:  A085216 A085217 A085218 * A085220 A085221 A085222 KEYWORD nonn,tabl AUTHOR Antti Karttunen Jun 23 2003 STATUS approved

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Last modified January 24 04:47 EST 2022. Contains 350534 sequences. (Running on oeis4.)