A213220 -id:A213220

Search: a213220 -id:a213220

Displaying 1-4 of 4 results found.

page 1

A221715

Start of n-th doubling run in A114183.

+10
7

1, 5, 3, 9, 33, 11, 13, 7, 21, 25, 20, 17, 23, 19, 49, 39, 35, 47, 27, 29, 15, 43, 37, 97, 55, 41, 51, 57, 85, 73, 193, 111, 59, 61, 31, 89, 53, 329, 145, 192, 221, 237, 87, 105, 81, 101, 113, 481, 175, 149, 69, 93, 77, 99, 79, 71, 67, 65, 45, 75, 195, 157, 141, 189, 109, 83, 103, 229, 121, 352, 849, 233, 345, 297, 137, 187, 309, 281, 379, 155, 199, 159

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

OFFSET

1,2

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..7328

MAPLE

# A114181

M:=10000; M2:=1000;

s1:={1}; v0:=[1]; v1:=[1]; v2:=[]; vi:=Array(1..M2);

t1:=1; r1:=1; vi[1]:=1;

for n from 2 to M do

t2:=floor(sqrt(t1));

if t2 in s1 then

v0:=[op(v0), 2*t1]; s1:={op(s1), 2*t1}; r1:=r1+1; t1:=2*t1;

if t1<=M2 then vi[t1]:=n; fi;

else

v0:=[op(v0), t2]; s1:={op(s1), t2}; v1:=[op(v1), t2]; v2:=[op(v2), r1]; r1:=1; t1:=t2;

if t1<=M2 then vi[t1]:=n; fi;

fi;

od:

# A114183:

[seq(v0[i], i=1..nops(v0))];

# A221715:

[seq(v1[i], i=1..nops(v1))];

# A221716:

[seq(v2[i], i=1..nops(v2))];

# A189419:

[seq(vi[i], i=1..M2)];

CROSSREFS

Cf. A114183, A189419, A221716, A213220.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 27 2013

STATUS

approved

A221716

Length of n-th doubling run in A114183.

+10
6

6, 2, 6, 8, 3, 5, 3, 7, 6, 5, 5, 6, 5, 8, 6, 6, 7, 5, 6, 4, 8, 6, 9, 6, 6, 7, 7, 8, 7, 10, 7, 6, 7, 5, 9, 6, 12, 7, 9, 9, 9, 6, 8, 7, 8, 8, 12, 7, 8, 6, 8, 7, 8, 7, 7, 7, 7, 6, 8, 10, 8, 8, 9, 7, 7, 8, 10, 7, 11, 12, 7, 10, 9, 7, 9, 10, 9, 10, 7, 9, 8, 9, 11, 11, 5, 8, 9, 8, 11, 10, 6, 8, 8, 6, 10, 7, 8, 9, 12, 8, 9, 12, 6, 8, 8, 11, 8, 9, 9, 8, 10, 9, 12

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

OFFSET

1,1

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..7327

MAPLE

See A221715.

CROSSREFS

Cf. A114183, A189419, A221715, A213220.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 27 2013

STATUS

approved

A213656

Value of A114183 at end of n-th doubling run.

+10
1

32, 10, 96, 1152, 132, 176, 52, 448, 672, 400, 320, 544, 368, 2432, 1568, 1248, 2240, 752, 864, 232, 1920, 1376, 9472, 3104, 1760, 2624, 3264, 7296, 5440, 37376, 12352, 3552, 3776, 976, 7936, 2848, 108544, 21056, 37120, 49152, 56576, 7584, 11136, 6720, 10368, 12928, 231424, 30784, 22400, 4768, 8832, 5952, 9856

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

OFFSET

1,1

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..7327

CROSSREFS

Cf. A114183, A221715, A221716, A213220.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 03 2013

STATUS

approved

A222802

When A114183 decreases in value for the n-th time, dropping to k (say), a(n) is the number of steps earlier that floor(k/2) appeared in A114183.

+10
1

5, 8, 12, 18, 19, 21, 25, 33, 36, 44, 53, 37, 53, 64, 14, 31, 32, 69, 71, 76, 77, 108, 120, 39, 93, 105, 123, 125, 157, 170, 52, 91, 93, 99, 190, 192, 89, 225, 238, 121, 72, 158, 251, 238, 251, 270, 205, 50, 209, 282, 284, 286, 287, 288, 289, 361, 385, 370, 281, 282, 340, 342, 344, 346, 309, 310, 312, 367, 460, 275

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

OFFSET

1,1

COMMENTS

The fact that, when a number k occurs in A114183, floor(k/2) has already appeared, is a key step in the proof that A114183 is a permutation of the natural numbers. This fact is obvious if k is the result of a doubling step. The present sequence is an attempt to gain insight into why it is true when k occurs at a square root step.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..7322

EXAMPLE

The first 50 terms of A114183 are:

1, 2, 4, 8, 16, 32, 5, 10, 3, 6, 12, 24, 48, 96, 9, 18, 36, 72, 144, 288, 576, 1152, 33, 66, 132, 11, 22, 44, 88, 176, 13, 26, 52, 7, 14, 28, 56, 112, 224, 448, 21, 42, 84, 168, 336, 672, 25, 50, 100, 200.

The sequence decreases from 32 to 5, from 10 to 3, from 96 to 9, and so on.

The values of k are therefore 5, 3, 9, 33, 11, 13, 7, 21, 25, ...

and the corresponding values of floor(k/2) are 2, 1, 4, 16, 5, 6, 3, 10, 12, ...

Since 2 appeared in A114183 5 steps before 5, a(1) = 5,

since 1 appeared 8 steps before 3, a(2) = 8,

since 4 appeared 12 steps before 9, a(3) = 12, and so on.

CROSSREFS

Cf. A114183, A221715, A221716, A213220.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 08 2013

STATUS

approved

page 1

Search completed in 0.004 seconds