A218787 -id:A218787 - cp's OEIS frontend

A218614 a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218778.

1, 2, 3, 5, 7, 9, 13, 21, 29, 37, 53, 69, 101, 85, 117, 181, 245, 309, 437, 565, 821, 693, 949, 1205, 1717, 1461, 1973, 2741, 3765, 2485, 3509, 5557, 7605, 9653, 13749, 17845, 26037, 21941, 30133, 38325, 54709, 46517, 62901, 87477, 120245, 79285, 112053, 144821

Offset: 1

Antti Karttunen, Nov 16 2012

The binary code is the same as used by function general-car-cdr of MIT/GNU Scheme: a zero bit represents a cdr operation (taking the right hand side branch in the binary tree), and a one bit represents a car (taking the left hand side branch in the binary tree). The bits are interpreted from LSB to MSB, and the most significant one bit, rather than being interpreted as an operation, signals the end of the binary code.

			As we must traverse to 4 in A218778-tree (see the example there) by first taking the left branch (car) from the root, resulting bit 1 as the least significant bit of the code, then by taking the right branch (cdr) from 3 to get to 4, resulting bit 0 as the second rightmost bit of the code, which when capped with an extra termination-one, results binary code 101, 5 in decimal, thus a(4)=5.

A. Karttunen, Table of n, a(n) for n = 1..1024
MIT/GNU Scheme 9.1. documentation, Function general-car-cdr

a(n) = A054429(A218615(n)). Superset of A218790. Used to construct A218778, A218779. Cf. also A218787, A218788

a(1)=1; for even n, a(n) = A004754(a(A011371(n))); for odd n, a(n) = A004755(a(A011371(n))).

A218615 a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218776.

Original entry on oeis.org

1, 3, 2, 6, 4, 14, 10, 26, 18, 58, 42, 122, 90, 106, 74, 202, 138, 458, 330, 970, 714, 842, 586, 1866, 1354, 1610, 1098, 3402, 2378, 3658, 2634, 6730, 4682, 14922, 10826, 31306, 23114, 27210, 19018, 59978, 43594, 51786, 35402, 109130, 76362, 117322, 84554, 248394

Offset: 1

Antti Karttunen, Nov 16 2012

The binary code is the same as used by function general-car-cdr of MIT/GNU Scheme: a zero bit represents a cdr operation (taking the right hand side branch in the binary tree), and a one bit represents a car (taking the left hand side branch in the binary tree). The bits are interpreted from LSB to MSB, and the most significant one bit, rather than being interpreted as an operation, signals the end of the binary code.

			As we can traverse to 4 in A218776-tree (see the example there) by taking first the right branch (cdr) from the root, resulting bit 0 as the least significant bit of the code, then by taking the left branch (car) from 3 to get to 4, resulting bit 1 as the second rightmost bit of the code, which when capped with an extra termination-one, results binary code 110, 6 in decimal, thus a(4)=6.

A. Karttunen, Table of n, a(n) for n = 1..1024
MIT/GNU Scheme 9.1. documentation, Function general-car-cdr

a(n) = A054429(A218614(n)). Superset of A218791. Used to construct A218776, A218777. Cf. also A179016, A218787, A218788

a(1)=1, for odd n, a(n) = A004754(a(A011371(n))), for even n, a(n) = A004755(a(A011371(n))).

A218790 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218782.

Original entry on oeis.org

1, 3, 5, 13, 21, 37, 53, 117, 181, 309, 437, 693, 949, 1717, 1461, 3509, 5557, 9653, 13749, 21941, 30133, 54709, 46517, 79285, 112053, 210357, 177589, 472501, 308661, 734645, 996789, 2045365, 3093941, 5191093, 7288245, 11482549, 15676853, 28259765, 24065461

Offset: 1

Antti Karttunen, Nov 16 2012

Antti Karttunen, Table of n, a(n) for n = 1..1024

Subset of A218614, i.e. a(n) = A218614(A005187(n)).

Also, a(n) = A054429(A218791(n)). Used to construct A218782, A218783. Cf. also A218787, A218788

a(n) = A218614(A005187(n)).

A218791 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218780.

Original entry on oeis.org

1, 2, 6, 10, 26, 58, 42, 74, 202, 458, 330, 842, 586, 1354, 1610, 2634, 6730, 14922, 10826, 27210, 19018, 43594, 51786, 117322, 84554, 182858, 215626, 313930, 477770, 838218, 576074, 1100362, 3197514, 7391818, 5294666, 13683274, 9488970, 22071882, 26266186

Offset: 1

Antti Karttunen, Nov 16 2012

A. Karttunen, Table of n, a(n) for n = 1..1024

Subset of A218615, i.e., a(n) = A218615(A005187(n)).
Also, a(n) = A054429(A218790(n)). (Note also how the first five or so terms are twice the terms in the beginning of A218790, shifted by one term.)
Used to construct A218780, A218781. Cf. also A218787, A218788.

a(n) = A218615(A005187(n)).

cp's OEIS Frontend

A218614 a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218778.

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A218615 a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218776.

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A218790 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218782.

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A218791 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218780.

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