MathDB

For a real number

x

in the interval

(0,1)

with decimal representation

0.a_1(x)a_2(x)...a_n(x)...,

denote by

n(x)

the smallest nonnegative integer such that \overline{a_{n(x)\plus{}1}a_{n(x)\plus{}2}a_{n(x)\plus{}3}a_{n(x)\plus{}4}}\equal{}1966 . Determine

\int_0^1n(x)dx

. (

\overline{abcd}

denotes the decimal number with digits

a,b,c,d .

) A. Renyi

Problem Statement