Identical-digit blocks in decimal representation of partition numbers

[Jonathan Post]

Ralf makes sense here.  Consecutive digits matter in Ramanujan-type
congruences specifically where blocks of K zeroes occur at the right-hand
end of the digit string, i.e. when P(n) is a multiple of 10^K. Using the
extended list of Plouffe (through n = 16456) we find:

101 values of P(n) with blocks of eactly 4 zeroes, of which 11 occur with
the zeroes at the right (599, 776, 1949, 2499, 4989, 7964, 8249, 12499,
12624, 14574, 16274); there appearing to be some structure here (i.e. 2499 +
10000 = 12499).

10 values of P(n) with blocks of eactly 5 zeroes, of which 1 occurs with the
zeroes at the right (11224).

There are well-known P(n) mod 5 congruences; the powers of 10 are relevant
to simultaneously mod 2 and mod 5.




On 8/9/06, Ralf Stephan <ralf at ark.in-berlin.de> wrote:
>
> > Me:  Am I the only seqfan who finds this kind of investigation
> > extremely repugnant?
>
> You're not. In this case, however, it could be a hint for more
> Ramanujan-type congruences. The problem is that this is not followed
> up by more serious research into the matter.
>
>
> Regards,
> ralf
>
>
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