login
A085203
Array A(x,y): Position of the totally balanced binary string obtained by concatenating the binary strings A014486(x) & A014486(y) in such a way that the latter is inserted after the least significant 1-bit of the former, followed by the remaining 0-bits, if any. Listed antidiagonalwise as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...
13
0, 1, 1, 2, 3, 2, 3, 5, 7, 3, 4, 8, 12, 8, 4, 5, 10, 21, 13, 17, 5, 6, 13, 26, 22, 31, 18, 6, 7, 15, 35, 27, 58, 32, 20, 7, 8, 18, 40, 36, 73, 59, 34, 21, 8, 9, 22, 49, 41, 100, 74, 62, 35, 22, 9, 10, 24, 63, 50, 115, 101, 76, 63, 36, 45, 10, 11, 27, 68, 64, 142, 116, 104, 77, 64, 87, 46
OFFSET
0,4
COMMENTS
This table is induced by the list-function 'app-to-xrt' whose Scheme-definition is given below, in the same way as A085201 is induced by the ordinary 'append'-function.
FORMULA
a(0, y) = y, a(x, y) = A057548(a(A072771(x), y)) if A072772(x)=0, otherwise A072764bi(A072771(x), a(A072772(x), y)).
a(x, y) = A080300(A085211bi(A014486(x), A014486(y))) = A085200(A085219bi(A071155(y), A071155(x))).
PROG
(MIT/GNU Scheme) (define (A085203bi x y) (A080300 (A085211bi (A014486 x) (A014486 y))))
(define (A085203 n) (A085203bi (A025581 n) (A002262 n)))
(define (A085204 n) (A085203bi (A002262 n) (A025581 n)))
(HERE IS THE CORRESPONDING FUNCTION FOR S-EXPRESSIONS): (define (app-to-xrt a b) (cond ((null? a) b) ((pair? (cdr a)) (cons (car a) (app-to-xrt (cdr a) b))) (else (cons (app-to-xrt (car a) b) (cdr a)))))
(AND THE DESTRUCTIVE VARIANT): (define (app-to-xrt! a b) (cond ((null? a) b) (else (let recurse ((a a) (b b)) (cond ((and (not (pair? (car a))) (not (pair? (cdr a)))) (set-car! a b)) ((pair? (cdr a)) (recurse (cdr a) b)) (else (recurse (car a) b)))) a)))
CROSSREFS
Transpose: A085204. Variant: A085201. Row 1: A085225, Column 1: A057548.
Sequence in context: A179969 A356861 A327717 * A251104 A199334 A330903
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Jun 23 2003
STATUS
approved