Keith Number Checker

Appears in own digit sequence

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About Keith Number Checker

A Keith number checker testing if n appears in the sequence starting with its digits, where each subsequent term is the sum of the previous d terms (d = number of digits). Also called repfigit numbers. Shows the full sequence. Client-side.

Keith Number Checker Features

  • Keith check
  • Sequence
  • Step display
  • Search range
  • List
Keith number: n-digit number N that appears in the sequence beginning with its digits, where each term is the sum of the previous n terms. 14: 1,4,5,9,14 ✓. 197: 1,9,7,17,33,57,107,197 ✓. Only 95 Keith numbers are known below 10^22.

How to Use

Enter number:

  • Keith?: Check membership
  • Sequence: Full digit sequence
  • Steps: How it's built

Known Keith Numbers

14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, ... Only ~95 are known below 10^22. Very rare!

Why So Rare?

For d-digit numbers, the sequence grows roughly like a d-step Fibonacci (base ~d-th root of d-bonacci constant). Most numbers are 'skipped over' by the fast-growing sequence. Probability ≈ d·log(2)/10^d.

Step-by-Step Instructions

  1. 1Enter number.
  2. 2Check Keith.
  3. 3View sequence.
  4. 4See growth.
  5. 5Search range.

Keith Number Checker — Frequently Asked Questions

How are Keith numbers found?+

No formula exists — must test each number. For N with digits d₁,...,dₖ: generate the sequence d₁,d₂,...,dₖ,d₁+...+dₖ,... until reaching or exceeding N. If you hit N exactly, it's a Keith number.

Why are Keith numbers rare?+

The sequence grows exponentially (like a d-bonacci sequence), so it jumps over almost all numbers. For 2-digit numbers: seq grows like Fibonacci (~φⁿ). For 3-digit: like tribonacci (~1.84ⁿ). Most numbers fall between terms.

Are Keith numbers related to Fibonacci?+

Yes! For 2-digit numbers, the sequence IS Fibonacci-like (each term = sum of 2 previous). Keith numbers generalize: for d-digit numbers, each term = sum of d previous. The 2-digit Keith numbers are exactly the Fibonacci-like numbers that equal a 2-digit term.

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