A085215 Square array A(x,y) = the number whose factorial expansion A007623 is that of x and y concatenated; zero expanded as empty string; read by ascending antidiagonals: A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...

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

Offset

0,4

Links

Table of n, a(n) for n=0..72.

Formula

A(x,y) = A322001(concat(A007623(x), A007623(y))), where A322001 is a left inverse of A007623. - M. F. Hasler, Nov 27 2018

Example

From M. F. Hasler, Nov 27 2018:
The array starts:
   0   1   2   3   4   5  6 ...
   1   3   8   9  10  11 30 ...
   2   7  26  27  28  29 ...
   3   9  32  33  34  ...
   4  13  50  51  ...
  (...)  (End)
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.

Prog

(MIT/GNU 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)))
(PARI) A085215(x, y)=A322001(eval(Str(A007623(x), A007623(y)))) \\ M. F. Hasler, Nov 27 2018

Crossrefs

Transpose: A085216. Variant: A085219. Can be used to compute A085201. Cf. A000142, A007623, A084558, A025581, A002262.

Sequence in context: A055375 A091533 A055376 * A076731 A347650 A341653

Adjacent sequences: A085212 A085213 A085214 * A085216 A085217 A085218

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 23 2003

Status

approved