A392064 Decimal expansion of the expected number of consecutive random decimal digits whose running sum first exceeds 9.

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

Offset

1,1

Comments

In general, digits {0,...,m} with threshold > m has expectation ((m+1)/m)^(m+1) and has limit e = A001113 as m -> infinity, that limit being the classical result for how many uniformly distributed values U(0,1) are needed to exceed 1.

Links

Table of n, a(n) for n=1..88.

Formula

Equals (10/9)^10.

For n >= 387420491, a(n) = a(n-387420489). - Michael S. Branicky, Dec 29 2025

Example

2.86797199079244131332225723124... .

Mathematica

RealDigits[[(10/9)^10], 10, 120][[1]]

Prog

(PARI) a(n) = lift(Mod(10, 34867844010)^(n%387420489 + 9)) \ 3486784401; \\ Kevin Ryde, Jan 03 2026

Crossrefs

Cf. A001113, A007953.

Cf. A000012, A021085, A021733: decimal expansions of powers of 10/9.

Sequence in context: A065473 A375506 A054029 * A197589 A124356 A277249

Adjacent sequences: A392061 A392062 A392063 * A392065 A392066 A392067

Keyword

nonn,cons,easy

Author

Bruce Nye, Dec 29 2025

Status

approved