A219649 -id:A219649 - cp's OEIS frontend

A219647 Positions of zeros in A219649.

0, 2, 5, 9, 13, 18, 23, 29, 36, 43, 51, 59, 67, 76, 85, 95, 105, 115, 126, 137, 148, 160, 172, 185, 198, 211, 225, 239, 253, 268, 283, 298, 314, 330, 347, 364, 382, 400, 418, 437, 456, 475, 495, 515, 535, 556, 577, 599, 621, 643, 666, 689, 712, 735, 759, 784

Offset: 0

Antti Karttunen, Nov 24 2012

nonn

Antti Karttunen, Table of n, a(n) for n = 0..10946

Analogous sequence for binary system: A213707, for factorial number system: A219657.

Cf. A219646, A219649.

Scheme
```
(define (A219647 n) (+ n (A219646 n)))
```

a(n) = n+A219646(n).

A219648 The infinite trunk of Zeckendorf beanstalk. The only infinite sequence such that a(n-1) = a(n) - number of 1's in Zeckendorf representation of a(n).

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 20, 22, 24, 27, 29, 33, 35, 37, 40, 42, 45, 47, 50, 54, 56, 58, 61, 63, 67, 70, 74, 76, 79, 83, 88, 90, 92, 95, 97, 101, 104, 108, 110, 113, 117, 121, 123, 126, 130, 134, 138, 143, 145, 147, 150, 152, 156, 159, 163, 165, 168

Offset: 0

Antti Karttunen, Nov 24 2012

nonn

a(n) tells in what number we end in n steps, when we start climbing up the infinite trunk of the "Zeckendorf beanstalk" from its root (zero).
There are many finite sequences such as 0,1,2; 0,1,2,4,5; etc. (see A219649) and as the length increases, so (necessarily) does the similarity to this infinite sequence.
There can be only one infinite trunk in "Zeckendorf beanstalk" as all paths downwards from numbers >= A000045(i) must pass through A000045(i)-1 (i.e. A000071(i)). This provides also a well-defined method to compute the sequence, for example, via a partially reversed version A261076.
See A014417 for the Fibonacci number system representation, also known as Zeckendorf expansion.

Antti Karttunen, Table of n, a(n) for n = 0..11817

Cf. A000045, A000071, A007895, A014417, A219641, A219649, A261076, A261102. For all n, A219642(a(n)) = n and A219643(n) <= a(n) <= A219645(n). Cf. also A261083 & A261084.

Other similarly constructed sequences: A179016, A219666, A255056.

(define (A219648 n) (A261076 (A261102 n)))

a(n) = A261076(A261102(n)).

A219659 Irregular table where row n (n >= 0) starts with n, the next term is A219651(n), and the successive terms are obtained by repeatedly subtracting the sum of digits in the previous term's factorial expansion, until zero is reached, after which the next row starts with one larger n.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 1, 0, 4, 2, 1, 0, 5, 2, 1, 0, 6, 5, 2, 1, 0, 7, 5, 2, 1, 0, 8, 6, 5, 2, 1, 0, 9, 6, 5, 2, 1, 0, 10, 7, 5, 2, 1, 0, 11, 7, 5, 2, 1, 0, 12, 10, 7, 5, 2, 1, 0, 13, 10, 7, 5, 2, 1, 0, 14, 11, 7, 5, 2, 1, 0, 15, 11, 7, 5, 2, 1, 0, 16, 12, 10, 7, 5, 2, 1, 0

Offset: 0

Antti Karttunen, Nov 25 2012

Rows converge towards A219666 (reversed).

See A007623 for the Factorial number system representation.

A. Karttunen, Rows 0..120, flattened

Cf. A007623, A034968, A219651, A219657. Analogous sequence for binary system: A218254, for Zeckendorf expansion: A219649.

cp's OEIS Frontend

A219647 Positions of zeros in A219649.

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A219648 The infinite trunk of Zeckendorf beanstalk. The only infinite sequence such that a(n-1) = a(n) - number of 1's in Zeckendorf representation of a(n).

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Programs

Scheme

Formula

A219659 Irregular table where row n (n >= 0) starts with n, the next term is A219651(n), and the successive terms are obtained by repeatedly subtracting the sum of digits in the previous term's factorial expansion, until zero is reached, after which the next row starts with one larger n.

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