A219647 -id:A219647 - cp's OEIS frontend

A219649 Irregular table, where row n (n >= 0) starts with n, the next term is A219641(n), and the successive terms are obtained by repeatedly subtracting the number of 1's in the previous term's Zeckendorf expansion, until zero is reached, after which the next row starts with one larger n.

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

Offset: 0

Antti Karttunen, Nov 24 2012

Rows converge towards A219648 (reversed).

See A014417 for the Fibonacci number system representation, also known as Zeckendorf expansion.

A. Karttunen, Rows 0..233, flattened

Cf. A007895, A014417, A219641, A219647. Analogous sequence for binary system: A218254, for factorial number system: A219659.

A219657 Positions of zeros in A219659.

Original entry on oeis.org

0, 2, 5, 8, 12, 16, 21, 26, 32, 38, 44, 50, 57, 64, 71, 78, 86, 94, 102, 110, 119, 128, 137, 146, 156, 166, 177, 188, 199, 210, 222, 234, 246, 258, 271, 284, 297, 310, 324, 338, 352, 366, 381, 396, 411, 426, 441, 456, 472, 488, 504, 520, 537, 554, 571, 588, 606

Offset: 0

Antti Karttunen, Nov 25 2012

nonn

Antti Karttunen, Table of n, a(n) for n = 0..10080

Cf. A219656, A219659. Analogous sequence for binary system: A213707, for Zeckendorf expansion: A219647.

Scheme
```
(define (A219657 n) (+ n (A219656 n)))
```

a(n) = n + A219656(n).

A219646 Partial sums of A219642.

Original entry on oeis.org

0, 1, 3, 6, 9, 13, 17, 22, 28, 34, 41, 48, 55, 63, 71, 80, 89, 98, 108, 118, 128, 139, 150, 162, 174, 186, 199, 212, 225, 239, 253, 267, 282, 297, 313, 329, 346, 363, 380, 398, 416, 434, 453, 472, 491, 511, 531, 552, 573, 594, 616, 638, 660, 682, 705, 729, 753

Offset: 0

Antti Karttunen, Nov 24 2012

nonn

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

Used to compute A219647. Analogous sequence for binary system: A213706, for factorial number system: A219656.

cp's OEIS Frontend

A219649 Irregular table, where row n (n >= 0) starts with n, the next term is A219641(n), and the successive terms are obtained by repeatedly subtracting the number of 1's in the previous term's Zeckendorf expansion, until zero is reached, after which the next row starts with one larger n.

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A219657 Positions of zeros in A219659.

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A219646 Partial sums of A219642.

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