A389885 Decimal expansion of 1/7142857.

0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, 0, 4, 4, 8, 0, 0, 0, 0, 0, 8, 9, 6, 0, 0, 0, 0, 1, 7, 9, 2, 0, 0, 0, 0, 3, 5, 8, 4, 0, 0, 0, 0, 7, 1, 6, 8, 0, 0, 0, 1, 4, 3, 3, 6, 0, 0, 0, 2, 8, 6, 7, 2

Offset

0,8

Comments

If divided in blocks of length 8, the value of each block is twice the value of the previous block. This doubling pattern breaks at the 23rd block, since after 23 doublings (at the 24th block) the value is > 10^8 - 1 and the overflow is carried over to the 23rd block.

Purely periodic with period A007732(7142857) = 3416138 and which is the linear recurrence order too. - Kevin Ryde, Nov 19 2025

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Dr Barker, My New Favourite Number, YouTube video, 2025.

Index entries for linear recurrences with constant coefficients, order 3416138.

Formula

Equals 7*Sum_{k >= 1} (2/10^8)^k.

Example

0.000000140000002800000056000001120000022400000448...

Mathematica

First[RealDigits[1/7142857, 10, 100, -1]]

Prog

(PARI) a(n) = lift(Mod(10, 71428570)^((n+1) % 3416138)) \ 7142857; \\ Kevin Ryde, Nov 19 2025

Crossrefs

Cf. A020806, A007732.

Sequence in context: A308428 A396549 A308276 * A340977 A180989 A075444

Adjacent sequences: A389882 A389883 A389884 * A389886 A389887 A389888

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 16 2025

Status

approved