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A057300 Binary counter with odd/even bit positions swapped; base 4 counter with 1's replaced by 2's and vice versa. 15
0, 2, 1, 3, 8, 10, 9, 11, 4, 6, 5, 7, 12, 14, 13, 15, 32, 34, 33, 35, 40, 42, 41, 43, 36, 38, 37, 39, 44, 46, 45, 47, 16, 18, 17, 19, 24, 26, 25, 27, 20, 22, 21, 23, 28, 30, 29, 31, 48, 50, 49, 51, 56, 58, 57, 59, 52, 54, 53, 55, 60, 62, 61, 63, 128, 130, 129, 131, 136, 138 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A self-inverse permutation of the integers.

It is not true in general that a(2n) = -2a(n) + 5n, a(2n+1) = -2a(n) + 5n + 2 as was originally conjectured.

Counterexamples: a(46) = 29; a(92) = 172; binary(172) = [1, 0, 1, 0, 1, 1, 0, 0], but binary(-2*29+5*92) = binary(402) = [1, 1, 0, 0, 1, 0, 0, 1, 0]. a(45) = 30; a(91) = 167; binary(167) = [1, 0, 1, 0, 0, 1, 1, 1], but -2*30+5*91+2=397 and binary(397) = [1, 1, 0, 0, 0, 1, 1, 0, 1] - Lambert Herrgesell (zero815(AT)googlemail.com), Jan 13 2007

a(n) = n if and only if n can be written as 3*Sum[d_i*4^k, 0 <= k < infinity], where d_i is either 0 or 1. - Jon Perry, Oct 06 2012

LINKS

Paul Tek, Table of n, a(n) for n = 0..16383

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(4n+k) = 4a(n) + a(k), 0 <= k <= 3. - Jon Perry, Oct 06 2012

EXAMPLE

a(31) = a(4*7+3) = 4*a(7) + a(3) = 4*11 + 3 = 47.

CROSSREFS

Cf. A057301.

Sequence in context: A078045 A202624 A145490 * A076655 A236438 A101486

Adjacent sequences:  A057297 A057298 A057299 * A057301 A057302 A057303

KEYWORD

easy,nonn

AUTHOR

Marc LeBrun, Aug 24 2000

STATUS

approved

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Last modified April 20 13:42 EDT 2014. Contains 240806 sequences.