숫자 수열 생성기
클래식 수열 생성, 알 수 없는 수열 식별, 또는 사용자 정의 수열 생성.
이 도구에 대해
피보나치, 루카스, 소수, 완전 제곱수, 삼각수, 오각수, 팩토리얼, 2의 거듭제곱, N의 거듭제곱, 등차 수열, 등비 수열 등 11가지 내장 생성기 중 선택하여 처음 20개 항과 폐형 공식 및 OEIS 참조 번호를 즉시 확인하세요. 식별 모드에서는 숫자 수열을 붙여 넣으면 도구가 일치하는 알려진 수열을 감지합니다. 사용자 정의 모드에서는 첫 번째 항과 공차 또는 공비를 지정하여 사용자 정의 수열의 다음 N개 항을 생성할 수 있습니다.
사용 방법
- 1 드롭다운에서 수열을 선택하면(예: 피보나치) 처음 20개 항, 공식, OEIS 참조가 즉시 나타납니다.
- 2 '식별' 탭으로 전환하고, 쉼표로 구분된 숫자 목록을 붙여 넣은 후 '식별'을 클릭하여 일치하는 내장 수열을 확인하세요.
- 3 '사용자 정의' 탭으로 전환하고, 시작 값, 단계, 항 수를 입력한 후 '생성'을 클릭하세요.
- 4 출력 옆의 '복사' 버튼으로 수열을 클립보드에 복사하세요.
What a number sequence generator does
A number sequence is an ordered list of numbers built by a rule. This tool does three related jobs: it generates the terms of well-known sequences, it tries to identify an unknown sequence you paste in, and it builds custom arithmetic or geometric progressions from your own starting values. Each built-in sequence comes with its defining formula and, where one exists, its reference number in the On-Line Encyclopedia of Integer Sequences (OEIS), so you can verify the math against an authoritative catalogue rather than taking the output on faith.
The sequences it knows, and their rules
The generator ships with eleven named patterns. The recursive and closed-form rules behind them are:
| Sequence | Rule | First terms |
|---|---|---|
| Fibonacci | F(n) = F(n-1) + F(n-2), F(0)=0, F(1)=1 | 0, 1, 1, 2, 3, 5, 8 |
| Lucas | same recurrence, L(0)=2, L(1)=1 | 2, 1, 3, 4, 7, 11, 18 |
| Primes | n-th number divisible only by 1 and itself | 2, 3, 5, 7, 11, 13 |
| Squares | a(n) = n² | 1, 4, 9, 16, 25 |
| Triangular | T(n) = n(n+1)/2 | 1, 3, 6, 10, 15 |
| Pentagonal | P(n) = n(3n-1)/2 | 1, 5, 12, 22, 35 |
| Factorial | a(n) = n! | 1, 1, 2, 6, 24, 120 |
| Powers of 2 / N | a(n) = Nⁿ from n=0 | 1, 2, 4, 8, 16 (N=2) |
The arithmetic option uses a(n) = a₀ + n·d and the geometric option uses a(n) = a₀ · rⁿ, where you choose the start, the common difference d, or the common ratio r.
A worked example
Pick Triangular Numbers and the tool generates the first 20 terms. Term 5 is T(5) = 5 × 6 / 2 = 15; term 6 is 6 × 7 / 2 = 21. Notice each term is the previous one plus its own index: 15 + 6 = 21. That is the visual meaning of "triangular" — stacking rows of 1, 2, 3, 4… dots. Switch to the geometric tab with start 1 and ratio 2 and you get the powers of two; change the ratio to 3 and the same machinery produces 1, 3, 9, 27, 81. One formula, many sequences.
Identifying a mystery sequence
Paste at least three comma-separated numbers into the Identify tab and the tool checks them against every built-in pattern, reporting each match with its formula and OEIS code. Give it 2, 1, 3, 4, 7 and it recognises the Lucas numbers; give it 1, 3, 6, 10 and it returns Triangular. For arithmetic and geometric guesses it infers the step or ratio from your first two numbers, so 5, 8, 11, 14 is identified as an arithmetic progression with difference 3. If nothing matches within a small tolerance, it says so honestly rather than inventing a rule — a useful signal that your sequence may be irregular, mistyped, or simply outside the built-in set.
Use cases
- Homework and self-study. Check whether your hand-computed terms are right, and see the closed-form formula next to the recurrence.
- Test data and puzzles. Generate a clean list of squares, primes, or factorials to seed unit tests, spreadsheets, or programming exercises, then copy it with one click.
- Spotting a pattern. When you have a few numbers from a problem and suspect there's a rule, the Identify tab is faster than guessing.
- Teaching. Demonstrate how Fibonacci and Lucas share a recurrence but differ only in their seeds, or how triangular numbers are partial sums of the integers.
Tips and common mistakes
- Three numbers is the minimum to identify. Two numbers fit infinitely many rules; the tool requires at least three and ignores anything that isn't a valid number.
- Factorials and powers grow explosively. By the twentieth term a factorial is astronomically large, and beyond a certain point standard floating-point arithmetic loses exactness. Treat very large terms as approximate.
- The Identify tab only knows its built-in list. "No match" means none of these eleven patterns fit — not that your sequence is meaningless. For an exhaustive search, look the terms up directly in the OEIS.
- Geometric ratios can be fractional. A ratio of 0.5 produces a halving sequence; the field accepts decimals, so you are not limited to whole-number growth.
Everything is computed in your browser as you type — no input is sent anywhere — so you can generate and identify sequences offline.