A085211 Array A(x,y): concatenation of the binary expansions of x & y in such a way that 'y' is inserted after the least significant 1-bit of 'x', 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), ... Zero is expanded as an empty string.

0, 1, 1, 2, 3, 2, 3, 6, 6, 3, 4, 7, 12, 7, 4, 5, 12, 14, 14, 12, 5, 6, 11, 24, 15, 24, 13, 6, 7, 14, 22, 28, 28, 26, 14, 7, 8, 15, 28, 23, 48, 29, 28, 15, 8, 9, 24, 30, 30, 44, 52, 30, 30, 24, 9, 10, 19, 48, 31, 56, 45, 56, 31, 48, 25, 10, 11, 22, 38, 56, 60, 58, 46, 60, 56, 50, 26, 11

Offset

0,4

Links

Table of n, a(n) for n=0..77.

Formula

a(0, y) = y, a(x, y) = A006519(x) * (y + ((2^A029837(y+1))*A000265(x))).

Example

A(8,3) = 56 = '1110000' in binary, is produced when '11' (binary expansion of 3) is inserted after the least significant (and only) 1-bit of '1000' (binary expansion of 8).

Prog

(MIT/GNU Scheme) (define (A085211bi x y) (cond ((zero? x) (A085207bi x y)) (else (* (+ (* (expt 2 (A029837 (1+ y))) (A000265 x)) y) (A006519 x)))))
(define (A085211 n) (A085211bi (A025581 n) (A002262 n)))
(define (A085212 n) (A085211bi (A002262 n) (A025581 n)))

Crossrefs

Same array in binary: A085213. Transpose: A085212. Variant: A085207 (normal concatenation). Can be used to compute A085203.

Sequence in context: A332553 A257302 A268715 * A085212 A079025 A165930

Adjacent sequences: A085208 A085209 A085210 * A085212 A085213 A085214

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 23 2003

Status

approved