A316628 -id:A316628 - cp's OEIS frontend

A324475 k appears t+1 times, where t is the number of trailing zeros in A324474(k).

1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 9, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 16, 16, 17, 17, 17, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 26, 27, 27, 28, 28, 29, 29, 29, 30, 31, 31, 31, 31, 31, 31, 32, 33, 34, 34

Offset: 1

Nathan Fox and N. J. A. Sloane, Mar 09 2019

Interesting because the recurrence is nested one layer deeper than the recurrences for A046699 and A316628.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Nathan Fox, Trees, Fibonacci Numbers, and Nested Recurrences, Rutgers University Experimental Math Seminar, Mar 07, 2019
Rémy Sigrist, PARI program for A324475

Cf. A324474.

A046699, A316628, A324473, A324477 have similar definitions.

PARI
```
See Links section.
```

For n>3, a(n) = a(n-a(n-1)) + a(n-1-a(n-2)-a(n-2-a(n-2))) + a(n-2-a(n-3)-a(n-3-a(n-3)) - a(n-3-a(n-3)-a(n-3-a(n-3)))). - Nathan Fox, Mar 09 2019 (This formula assumes that a(0) = 0. - Rémy Sigrist, Mar 14 2021)

Data corrected and more terms from Rémy Sigrist, Mar 14 2021

A324477 k appears t+1 times, where t = A364377(k) is the number of trailing zeros in the greedy Jacobsthal representation of k, A265747(k).

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 11, 11, 12, 13, 14, 14, 15, 16, 16, 16, 17, 18, 19, 19, 20, 21, 21, 21, 21, 21, 22, 23, 24, 24, 25, 26, 26, 26, 27, 28, 29, 29, 30, 31, 31, 31, 32, 32, 32, 32, 33, 34, 35, 35, 36, 37, 37, 37, 38, 39, 40, 40

Offset: 1

Nathan Fox and N. J. A. Sloane, Mar 09 2019

Amiram Eldar, Table of n, a(n) for n = 1..10000
Nathan Fox, Trees, Fibonacci Numbers, and Nested Recurrences, Rutgers University Experimental Math Seminar, Mar 07, 2019.

Cf. A001045, A265747, A364377.

A046699, A316628, A324473 and A324475 have similar definitions.

Table[Table[k, {IntegerExponent[A265747[k], 10] + 1}], {k, 1, 40}] // Flatten (* Amiram Eldar, Jul 21 2023 using A265747[n] *)

More terms from Amiram Eldar, Jul 21 2023

A324473 k appears A278045(k)+1 times.

Original entry on oeis.org

1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 11, 11, 1, 13, 13, 13, 13, 14, 15, 15, 16, 17, 17, 17, 18, 189, 19, 20, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30

Offset: 1

N. J. A. Sloane, Mar 07 2019

nonn

Each k appears one more times than the number of trailing zeros in the tribonacci representation of n (see A278038).

This is related to the tribonacci representation of n in the same way as A046699 (without its initial term) is related to the binary representation of n and as A316628 is to the Zeckendorf representation of n.

Nathan Fox, Trees, Fibonacci Numbers, and Nested Recurrences, Rutgers University Experimental Math Seminar, Mar 07, 2019

Cf. A046699, A278038, A278045, A316628.

cp's OEIS Frontend

A324475 k appears t+1 times, where t is the number of trailing zeros in A324474(k).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula

Extensions

A324477 k appears t+1 times, where t = A364377(k) is the number of trailing zeros in the greedy Jacobsthal representation of k, A265747(k).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A324473 k appears A278045(k)+1 times.

Views

Author

Keywords

Comments

Links

Crossrefs