Calculators
Jacobsthal Number Calculator
Calculate exact Jacobsthal numbers for indices 0 to 1000 privately in your browser, with the next term and digit count.
Calculate exact terms in the Jacobsthal sequence.
Jacobsthal numbers start with J(0) = 0 and J(1) = 1. Each later term adds the preceding term to twice the earlier term: J(n) = J(n − 1) + 2 × J(n − 2). The sequence begins 0, 1, 1, 3, 5, 11, 21, 43. For example, J(5) = 5 + 2 × 3 = 11. The closed form is J(n) = (2^n − (−1)^n) ÷ 3. Enter an index from 0 to 1000 using one to four digits; leading zeros and surrounding whitespace are accepted. Signs, decimals, separators and scientific notation are rejected. Exact BigInt arithmetic preserves every digit. Results include the selected term, its decimal digit count and the next term. Zero has one digit. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How are Jacobsthal numbers calculated?
Start with J(0) = 0 and J(1) = 1. Each subsequent term is the preceding term plus twice the earlier term. For example, J(5) = 5 + 2 × 3 = 11.
How do Jacobsthal and Fibonacci numbers differ?
Jacobsthal numbers add the preceding term to twice the earlier term. Fibonacci numbers simply add the preceding two terms.
Are large results exact?
Yes. BigInt arithmetic preserves every digit. Results include the selected term, its decimal digit count and the next term without rounding.
Which inputs are supported?
Enter an index from 0 to 1000 using one to four digits. Leading zeros and surrounding whitespace are accepted. Signs, decimals, separators and scientific notation are rejected. Calculations stay in your browser.