[seqfan] Sum of a(n) first digits of S is a(n+1)

[Eric Angelini]

Hello SeqFans,

... I couldn't get to sleep yesterday, 'cause I was
trying to find more terms with my poor new 2010 brain...

a) the sum of the a(n) first digits of S is a(n+1)
b) always use the smallest available integer not leading
   to a contradiction

S = 4, 10, 50, 59, 98, 99, ...

Could it be that no such S is infinite?

Explanation:

 '4' says: "The first  4 digits of S sum up to 10" (--true)
'10' says: "The first 10 digits of S sum up to 50" (--true)
'50' says: "The first 50 digits of S sum up to 58" (--possible)
'59' says: "The first 59 digits of S sum up to 98" (--possible)
'98' says: "The first 98 digits of S sum up to 99" (--?)
etc. (?)

--> This start doesn't work:

    S = 4, 10, 50, 58, 99, 900, ...

--> No S can start with 1, 2 or 3

--> Other 4-starts for S:

    S = 4, 11, 50, ...
    S = 4, 12, 50, ...
    S = 4, 13, 50, ...
    ...
    S = 4, 19, 50, ...

--> More 4-starts for S:

    S = 4, 11, 51, ...
    S = 4, 11, 52, ...
    S = 4, 11, 53, ...
    ...

Help me finding sleep tonight!
;-)
Best,
É.