A389885 - OEIS

%I #29 Nov 19 2025 09:08:52

%S 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,

%T 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,

%U 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

%N Decimal expansion of 1/7142857.

%C 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.

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

%H Paolo Xausa, <a href="/A389885/b389885.txt">Table of n, a(n) for n = 0..10000</a>

%H Dr Barker, <a href="https://www.youtube.com/watch?v=iWQIvVrfOwE">My New Favourite Number</a>, YouTube video, 2025.

%H <a href="/index/Rec#order_3416138">Index entries for linear recurrences with constant coefficients</a>, order 3416138.

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

%e 0.000000140000002800000056000001120000022400000448...

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

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

%Y Cf. A020806, A007732.

%K nonn,cons,easy

%O 0,8

%A _Paolo Xausa_, Nov 16 2025