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), ...

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.

Links

Table of n, a(n) for n=0..76.

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

(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.

Cf. also A014486, A080300, A025581, A002262.

Sequence in context: A356861 A327717 A383444 * A251104 A199334 A330903

Adjacent sequences: A085200 A085201 A085202 * A085204 A085205 A085206

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 23 2003

Status

approved