Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000827
Mapping
St000827: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 2
1 => 3
00 => 4
01 => 5
10 => 6
11 => 7
000 => 8
001 => 9
010 => 10
011 => 11
100 => 12
101 => 13
110 => 14
111 => 15
0000 => 16
0001 => 17
0010 => 18
0011 => 19
0100 => 20
0101 => 21
0110 => 22
0111 => 23
1000 => 24
1001 => 25
1010 => 26
1011 => 27
1100 => 28
1101 => 29
1110 => 30
1111 => 31
00000 => 32
00001 => 33
00010 => 34
00011 => 35
00100 => 36
00101 => 37
00110 => 38
00111 => 39
01000 => 40
01001 => 41
01010 => 42
01011 => 43
01100 => 44
01101 => 45
01110 => 46
01111 => 47
10000 => 48
10001 => 49
10010 => 50
10011 => 51
Description
The decimal representation of a binary word with a leading 1. This statistic is obtained by prepending $1$ to the binary word and interpreting it as a number in binary.
Matching statistic: St000289
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000289: Binary words ⟶ ℤResult quality: 42% ●values known / values provided: 42%●distinct values known / distinct values provided: 42%
Values
0 => [2] => 10 => 2
1 => [1,1] => 11 => 3
00 => [3] => 100 => 4
01 => [2,1] => 101 => 5
10 => [1,2] => 110 => 6
11 => [1,1,1] => 111 => 7
000 => [4] => 1000 => 8
001 => [3,1] => 1001 => 9
010 => [2,2] => 1010 => 10
011 => [2,1,1] => 1011 => 11
100 => [1,3] => 1100 => 12
101 => [1,2,1] => 1101 => 13
110 => [1,1,2] => 1110 => 14
111 => [1,1,1,1] => 1111 => 15
0000 => [5] => 10000 => 16
0001 => [4,1] => 10001 => 17
0010 => [3,2] => 10010 => 18
0011 => [3,1,1] => 10011 => 19
0100 => [2,3] => 10100 => 20
0101 => [2,2,1] => 10101 => 21
0110 => [2,1,2] => 10110 => 22
0111 => [2,1,1,1] => 10111 => 23
1000 => [1,4] => 11000 => 24
1001 => [1,3,1] => 11001 => 25
1010 => [1,2,2] => 11010 => 26
1011 => [1,2,1,1] => 11011 => 27
1100 => [1,1,3] => 11100 => 28
1101 => [1,1,2,1] => 11101 => 29
1110 => [1,1,1,2] => 11110 => 30
1111 => [1,1,1,1,1] => 11111 => 31
00000 => [6] => 100000 => 32
00001 => [5,1] => 100001 => 33
00010 => [4,2] => 100010 => 34
00011 => [4,1,1] => 100011 => 35
00100 => [3,3] => 100100 => 36
00101 => [3,2,1] => 100101 => 37
00110 => [3,1,2] => 100110 => 38
00111 => [3,1,1,1] => 100111 => 39
01000 => [2,4] => 101000 => 40
01001 => [2,3,1] => 101001 => 41
01010 => [2,2,2] => 101010 => 42
01011 => [2,2,1,1] => 101011 => 43
01100 => [2,1,3] => 101100 => 44
01101 => [2,1,2,1] => 101101 => 45
01110 => [2,1,1,2] => 101110 => 46
01111 => [2,1,1,1,1] => 101111 => 47
10000 => [1,5] => 110000 => 48
10001 => [1,4,1] => 110001 => 49
10010 => [1,3,2] => 110010 => 50
10011 => [1,3,1,1] => 110011 => 51
000000000 => [10] => 1000000000 => ? = 512
000000001 => [9,1] => 1000000001 => ? = 513
000000010 => [8,2] => 1000000010 => ? = 514
000000011 => [8,1,1] => 1000000011 => ? = 515
000000100 => [7,3] => 1000000100 => ? = 516
000000101 => [7,2,1] => 1000000101 => ? = 517
000000110 => [7,1,2] => 1000000110 => ? = 518
000000111 => [7,1,1,1] => 1000000111 => ? = 519
000001000 => [6,4] => 1000001000 => ? = 520
000001001 => [6,3,1] => 1000001001 => ? = 521
000001010 => [6,2,2] => 1000001010 => ? = 522
000001011 => [6,2,1,1] => 1000001011 => ? = 523
000001100 => [6,1,3] => 1000001100 => ? = 524
000001101 => [6,1,2,1] => 1000001101 => ? = 525
000001110 => [6,1,1,2] => 1000001110 => ? = 526
000001111 => [6,1,1,1,1] => 1000001111 => ? = 527
000010000 => [5,5] => 1000010000 => ? = 528
000010001 => [5,4,1] => 1000010001 => ? = 529
000010010 => [5,3,2] => 1000010010 => ? = 530
000010011 => [5,3,1,1] => 1000010011 => ? = 531
000010100 => [5,2,3] => 1000010100 => ? = 532
000010101 => [5,2,2,1] => 1000010101 => ? = 533
000010110 => [5,2,1,2] => 1000010110 => ? = 534
000010111 => [5,2,1,1,1] => 1000010111 => ? = 535
000011000 => [5,1,4] => 1000011000 => ? = 536
000011001 => [5,1,3,1] => 1000011001 => ? = 537
000011010 => [5,1,2,2] => 1000011010 => ? = 538
000011011 => [5,1,2,1,1] => 1000011011 => ? = 539
000011100 => [5,1,1,3] => 1000011100 => ? = 540
000011101 => [5,1,1,2,1] => 1000011101 => ? = 541
000011110 => [5,1,1,1,2] => 1000011110 => ? = 542
000011111 => [5,1,1,1,1,1] => 1000011111 => ? = 543
000100000 => [4,6] => 1000100000 => ? = 544
000100001 => [4,5,1] => 1000100001 => ? = 545
000100010 => [4,4,2] => 1000100010 => ? = 546
000100011 => [4,4,1,1] => 1000100011 => ? = 547
000100100 => [4,3,3] => 1000100100 => ? = 548
000100101 => [4,3,2,1] => 1000100101 => ? = 549
000100110 => [4,3,1,2] => 1000100110 => ? = 550
000100111 => [4,3,1,1,1] => 1000100111 => ? = 551
000101000 => [4,2,4] => 1000101000 => ? = 552
000101001 => [4,2,3,1] => 1000101001 => ? = 553
000101010 => [4,2,2,2] => 1000101010 => ? = 554
000101011 => [4,2,2,1,1] => 1000101011 => ? = 555
000101100 => [4,2,1,3] => 1000101100 => ? = 556
000101101 => [4,2,1,2,1] => 1000101101 => ? = 557
000101110 => [4,2,1,1,2] => 1000101110 => ? = 558
000101111 => [4,2,1,1,1,1] => 1000101111 => ? = 559
000110000 => [4,1,5] => 1000110000 => ? = 560
000110001 => [4,1,4,1] => 1000110001 => ? = 561
Description
The decimal representation of a binary word.