A181935 -id:A181935

A212439

a(n) = 2*n + A181935(n) mod 2.

+20
4

1, 3, 5, 6, 8, 11, 13, 15, 17, 19, 20, 22, 24, 27, 29, 30, 32, 35, 37, 38, 40, 42, 45, 47, 49, 51, 52, 54, 56, 59, 61, 63, 65, 67, 69, 70, 72, 74, 77, 79, 81, 83, 85, 86, 88, 90, 93, 94, 96, 99, 101, 102, 104, 106, 108, 111, 113, 115, 116, 118, 120, 123, 125

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

a(n) = 2*n + A212412(n): concatenation of binary representation of n and the parity of its curling number;

A212444 gives iterations starting from 0.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..8191

Benjamin Chaffin and N. J. A. Sloane, The Curling Number Conjecture, preprint.

Index entries for sequences related to binary expansion of n

PROG

(Haskell)

a212439 n = 2 * n + a212412 n

CROSSREFS

Cf. A014601, A007088, A181935, A212412, A212444.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 17 2012

STATUS

approved

A212440

Numbers with even curling numbers of their binary representations, cf. A181935.

+20
4

3, 4, 10, 11, 12, 15, 16, 19, 20, 21, 26, 27, 28, 35, 36, 37, 43, 44, 45, 47, 48, 51, 52, 53, 54, 58, 59, 60, 63, 64, 67, 68, 69, 73, 74, 75, 76, 79, 80, 82, 83, 84, 90, 91, 92, 99, 100, 101, 107, 108, 109, 111, 112, 115, 116, 117, 118, 122, 123, 124, 131

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A212412(a(n)) = 0; complement of A212441.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

PROG

(Haskell)

a212440 n = a212440_list !! (n-1)

a212440_list = filter (even . a181935) [0..]

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 17 2012

STATUS

approved

A212441

Numbers with odd curling numbers of their binary representations, cf. A181935.

+20
4

0, 1, 2, 5, 6, 7, 8, 9, 13, 14, 17, 18, 22, 23, 24, 25, 29, 30, 31, 32, 33, 34, 38, 39, 40, 41, 42, 46, 49, 50, 55, 56, 57, 61, 62, 65, 66, 70, 71, 72, 77, 78, 81, 85, 86, 87, 88, 89, 93, 94, 95, 96, 97, 98, 102, 103, 104, 105, 106, 110, 113, 114, 119, 120

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

A212412(a(n)) = 1; complement of A212440.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

PROG

(Haskell)

a212441 n = a212441_list !! (n-1)

a212441_list = filter (odd . a181935) [0..]

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 17 2012

STATUS

approved

A212412

Parity of curling number of binary expansion of n.

+10
5

1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0

COMMENTS

a(n) = A181935(n) mod 2;

a(A212440(n)) = 0 and a(A212441(n)) = 1;

A212439(n) = 2*n + a(n).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = A000035(A181935(n)). - Omar E. Pol, Oct 28 2013

PROG

(Haskell)

a212412 = (`mod` 2) . a181935

CROSSREFS

Cf. A212444.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 17 2012

STATUS

approved

A224765

Denominator of fractional curling number of binary expansion of n.

+10
4

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 3, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 6, 2, 1, 1, 1, 5, 1, 1, 3, 2, 1, 1, 3, 5, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

COMMENTS

See A224762 for definition and Maple program.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

EXAMPLE

1, 1, 1, 2, 2, 3/2, 1, 3, 3, 4/3, 2, 2, 2, 3/2, 1, 4, 4, 5/4, 5/3, 2, 2, 5/2, 5/3, 3, 3, 4/3, 2, 2, 2, 3/2, 1, 5, 5, 6/5, 3/2, 2, 2, 2, 3/2, 3, 3, 5/3, 3, 2, 2, 2, 3/2, 4, 4, 5/4, 5/3, 2, 2, 5/2, 2, 3, 3, 4/3, 2, 2, 2, 3/2, 1, 6, 6, 7/6, 3/2, 2, ...

For example, 18 = 10010 in binary has fractional curling number 5/4.

CROSSREFS

Cf. A224764, A224762, A181935.

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Apr 26 2013

STATUS

approved

A212444

Iterates A212439, starting from 0.

+10
3

0, 1, 3, 6, 13, 27, 54, 108, 216, 433, 867, 1734, 3469, 6939, 13878, 27756, 55512, 111025, 222050, 444101, 888202, 1776404, 3552808, 7105617, 14211235, 28422470, 56844941, 113689883, 227379766, 454759532, 909519064, 1819038129, 3638076259, 7276152518

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

2*a(n) <= a(n+1) <= 2*a(n) + 1.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..100

Benjamin Chaffin and N. J. A. Sloane, The Curling Number Conjecture, preprint.

FORMULA

a(n+1) = A212439(a(n)) = 2*a(n) + A181935(a(n)) mod 2, a(0) = 0.

PROG

(Haskell)

a212444 n = a212444_list !! n

a212444_list = iterate a212439 0

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 17 2012

STATUS

approved

A224764

Numerator of fractional curling number of binary expansion of n.

+10
3

1, 1, 1, 2, 2, 3, 1, 3, 3, 4, 2, 2, 2, 3, 1, 4, 4, 5, 5, 2, 2, 5, 5, 3, 3, 4, 2, 2, 2, 3, 1, 5, 5, 6, 3, 2, 2, 2, 3, 3, 3, 5, 3, 2, 2, 2, 3, 4, 4, 5, 5, 2, 2, 5, 2, 3, 3, 4, 2, 2, 2, 3, 1, 6, 6, 7, 3, 2, 2, 2, 7, 3, 3, 7, 5, 2, 2, 5, 7, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

See A224762 for definition and Maple program.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

EXAMPLE

1, 1, 1, 2, 2, 3/2, 1, 3, 3, 4/3, 2, 2, 2, 3/2, 1, 4, 4, 5/4, 5/3, 2, 2, 5/2, 5/3, 3, 3, 4/3, 2, 2, 2, 3/2, 1, 5, 5, 6/5, 3/2, 2, 2, 2, 3/2, 3, 3, 5/3, 3, 2, 2, 2, 3/2, 4, 4, 5/4, 5/3, 2, 2, 5/2, 2, 3, 3, 4/3, 2, 2, 2, 3/2, 1, 6, 6, 7/6, 3/2, 2, ...

For example, 18 = 10010 in binary has fractional curling number 5/4.

CROSSREFS

Cf. A224765, A224762, A181935.

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Apr 26 2013

STATUS

approved