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

[hv at crypt.org]

"Eric Angelini" <Eric.Angelini at kntv.be> wrote:
:
: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
[snip]

Why not? By the definition, I think a(n)=1 for all n should work.

Hugo