In 2018 Ondrej Janicko from Slovakia derived reverse Fibonacci sequence . It starts with numbers 0, 1, 8, 56, 384, 2624, 17920, 122368, and is defined by the recurrence relation:
Consecutive numbers in reverse Fibonacci sequence aproximate to number j = 6,828427112475… wich is reverse Fibonaccio ratio. Exact calculation of reverse Fibonaccio ratio is j = 4 + sqrt(8) = 6,828427112475…
The reverse Fibonacci sequence is derived from 24 repeated line of the sum of the digits of the classic Fibonacci sequence. The situation show folowing table.
| Fibonacci sequence | sum of digits | reverse Fibonacci sequence | |
|---|---|---|---|
| 1. | 1 | 1 | 2734013306883801088 |
| 2. | 1 | 1 | 400386978866003968 |
| 3. | 2 | 2 | 58635315505528832 |
| 4. | 3 | 3 | 8586943147278336 |
| 5. | 5 | 5 | 1257528709087232 |
| 6. | 8 | 8 | 184160815677440 |
| 7. | 13 | 4 | 26969727041536 |
| 8. | 21 | 3 | 3949625081856 |
| 9. | 34 | 7 | 578409201664 |
| 10. | 55 | 1 | 84706066432 |
| 11. | 89 | 8 | 12404916224 |
| 12. | 144 | 9(0) | 1816657920 |
| 13. | 233 | 8 | 266043392 |
| 14. | 377 | 8 | 38961152 |
| 15. | 610 | 7 | 5705728 |
| 16. | 987 | 6 | 835584 |
| 17. | 1597 | 4 | 122368 |
| 18. | 2584 | 1 | 1792 |
| 19. | 4181 | 5 | 2624 |
| 20. | 6765 | 6 | 384 |
| 21. | 10946 | 2 | 56 |
| 22. | 17711 | 8 | 8 |
| 23. | 28657 | 1 | 1 |
| 24. | 46368 | 9(0) | 0 |
- Jim Schellnack
- Jim Schultz
- Jim's clover
- Jim Scobie
- Jim Scott (American football)
- Jim Scott (bowls)
- Jim Scott Fish House
- Jim Scott Fishhouse
- Jim Scott (trade unionist)
- Jim Scott (Virginia)
- Jim Sebesta
- Jim Selman
- Jim Semonik
- Jim Seymour
- Jim Seymour (athlete)
- Jim Seymour (disambiguation)
- Jim Seymour (hurdler)
- Jim Sharpe
- Jim Sharpe (historian)
- Jim Sharrow
- Jim Shaw (swimmer)
- Jim Shea (politician)
- Jim Shelton (footballer)
- Jim Shepherd
- Jim Sherman (baseball)