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.

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

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

Table of n, a(n) for n=0..70.

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

(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 A384284

Adjacent sequences: A085216 A085217 A085218 * A085220 A085221 A085222

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 23 2003

Status

approved