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A085215
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Array A(x,y): 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.
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4
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0, 1, 1, 2, 3, 2, 3, 7, 8, 3, 4, 9, 26, 9, 4, 5, 13, 32, 27, 10, 5, 6, 15, 50, 33, 28, 11, 6, 7, 25, 56, 51, 34, 29, 30, 7, 8, 27, 122, 57, 52, 35, 126, 31, 8, 9, 31, 128, 123, 58, 53, 150, 127, 32, 9, 10, 33, 146, 129, 124, 59, 246, 151, 128, 33, 10, 11, 37, 152, 147, 130, 125, 270
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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EXAMPLE
| A(4,3) = 51 which has a factorial expansion '2011' (2*24+0*6+1*2+1*1), a concatenation of factorial expansions of 4, '20' and of 3, '11'. Similarly, A(3,4) = 34 which has a factorial expansion '1120' (1*24+1*6+2*2+0*1). See A085217 for the corresponding factorial expansions.
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PROG
| (MIT Scheme) (define (A085215bi x y) (let loop ((x x) (y y) (i 2) (j (1+ (A084558 y)))) (cond ((zero? x) y) (else (loop (floor->exact (/ x i)) (+ (* (A000142 j) (modulo x i)) y) (1+ i) (1+ j))))))
(define (A085215 n) (A085215bi (A025581 n) (A002262 n)))
(define (A085216 n) (A085215bi (A002262 n) (A025581 n)))
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CROSSREFS
| Transpose: A085216. Variant: A085219. Can be used to compute A085201. Cf. A000142, A007623, A084558, A025581, A002262.
Sequence in context: A055375 A091533 A055376 * A076731 A085216 A102310
Adjacent sequences: A085212 A085213 A085214 * A085216 A085217 A085218
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KEYWORD
| nonn,tabl
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AUTHOR
| Antti Karttunen (HisFirstname.HisSurname(AT)iki.fi) Jun 23 2003
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