142857

142857 is a six-digit integer notable for its role in modular arithmetic and decimal expansions. In base 10, it appears as the repeating block in the decimal expansion of 1/7: 0.142857142857..., a sequence known as the repetend of 1/7.

142857 is a cyclic number: multiples 2 through 6 are permutations of the same digits. Specifically, 2 × 142857 = 285714, 3 × 142857 = 428571, 4 × 142857 = 571428, 5 × 142857 = 714285, 6 × 142857 = 857142. Each product is a cyclic rotation of 142857.

The number is tightly linked to the relationship 7 × 142857 = 999999, equivalently 142857 = (10^6 − 1)/7. The six-digit cycle is the full repetend for 1/7 because 7 is a full reptend prime in base 10, giving a repeating period of 6 digits.

The sum of its digits is 27; the number is divisible by 27 (142857 / 27 = 5291), so it is a Harshad (Niven) number in base 10.

Because of its rotation property, 142857 is frequently cited as the canonical example of a cyclic number and appears in discussions of prime reciprocals, modular arithmetic, and recreational number theory.