A219648 -id:A219648 - cp's OEIS frontend

A261076 The infinite trunk of Zeckendorf (Fibonacci) beanstalk, with reversed subsections.

0, 1, 2, 4, 7, 5, 12, 9, 20, 17, 14, 33, 29, 27, 24, 22, 54, 50, 47, 45, 42, 40, 37, 35, 88, 83, 79, 76, 74, 70, 67, 63, 61, 58, 56, 143, 138, 134, 130, 126, 123, 121, 117, 113, 110, 108, 104, 101, 97, 95, 92, 90, 232, 226, 221, 217, 213, 209, 205, 201, 198, 193, 189, 185, 181, 178, 176, 172, 168, 165, 163, 159, 156, 152, 150, 147, 145

Offset: 0

Antti Karttunen, Aug 09 2015

This can be viewed as an irregular table: after the initial zero on row 0, start each row n with k = F(n+2)-1 and subtract repeatedly the number of "1-fibits" (number of terms in Zeckendorf expansion of k) from k to get successive terms, until the number that has already been listed (which is always F(n+1)-1) is encountered, which is not listed second time, but instead, the current row is finished and the next row starts with (F(n+3))-1, with the same process repeated. Here F(n) = the n-th Fibonacci number, A000045(n).

			As an irregular table, the sequence looks like:
  0;
  1;
  2;
  4;
  7, 5;
  12, 9;
  20, 17, 14;
  33, 29, 27, 24, 22;
  54, 50, 47, 45, 42, 40, 37, 35;
  ...
After zero, each row n is A261091(n) elements long.

Antti Karttunen, Table of n, a(n) for n = 0..11817; rows 0 .. 23 of the irregular table.
Indranil Ghosh, Python program to generate the sequence

Cf. A000045, A000071, A007895, A072649, A219641, A219648, A261091, A261102.

Cf. A218616 (analogous sequence for base-2).

For n <= 2, a(n) = n; for n >= 3, if A219641(a(n-1)) = F(k)-1 [i.e., one less than some Fibonacci number F(k)] then a(n) = F(k+2)-1, otherwise a(n) = A219641(a(n-1)).
As a composition:
a(n) = A219648(A261102(n)).

A261101 After zero, each n occurs A261091(n) times.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Aug 09 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..7624

Auxiliary sequence for constructing A261102 and A219648.

Cf. A261081.

(define (A261101 n) (let loop ((k 0)) (if (>= (A261081 k) n) k (loop (+ 1 k)))))

cp's OEIS Frontend

A261076 The infinite trunk of Zeckendorf (Fibonacci) beanstalk, with reversed subsections.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula