MathDB

For a positive integer

a

a'

is the integer obtained by the following method: the decimal writing of

a'

is the inverse of the decimal writing of

a

(the decimal writing of

a'

can begin by zeros, but not the one of

a

); for instance if

a=2370

a'=0732

, that is

732

. Let

a_{1}

be a positive integer, and

(a_{n})_{n \geq 1}

the sequence defined by

a_{1}

and the following formula for

n \geq 1

a_{n+1}=a_{n}+a'_{n}.

Can

a_{7}

be prime?

Problem Statement