# [seqfan] Re: A (new) problem

Max Alekseyev maxale at gmail.com
Wed Apr 28 00:06:16 CEST 2010

```On Mon, Apr 26, 2010 at 12:25 PM, Vladimir Shevelev <shevelev at bgu.ac.il> wrote:

> Since you obtained a proof of my conjecture and many terms of the sequence, then I ask you to enter it into OEIS (together with your proof as a main comment).

I've just submitted two sequences (quoted below).
Please also notice related sequences A176774 and A176775 that are

Regards,
Max

%I A176873
%S A176873 3,3,3,3,3,4,3,3,4,3,3,3,3,3,4,3,3,4,3,4,3,3,3,5,3,3,4,3,3,3,3,3,4,5,3,
%T A176873 4,3,3,3,3,4,4,3,3,4,3,3,5,3,3,4,3,4,4,4,3,3,3,3,4,3,3,7,5,3,3,3,3,4,3,
%U A176873 3,4,3,3,4,4,3,4,3,3,4,3,4,3,3,4,5,3,3,4,3,3,3,3,3,4,4,3,4,3,3,3,3,4,4
%N A176873 Smallest possible integer m>=3 such that n is the sum of
an m-gonal number and a k-gonal number for some k<=m.
%F A176873 a(n) = min max(A176774(i),A176774(n-i)), where min is taken
over i=0,1,...,n under the assumption that A176774(2) = +infinity.
%Y A176873 Cf. A176774, A176874
%K A176873 nonn
%O A176873 0,1
%A A176873 Max Alekseyev (maxale(AT)gmail.com), Apr 27 2010

%I A176874
%S A176874 0,5,23,62,62,723,1578,1578,8139,39644,94323,94323,1317783,1680515,
%T A176874 2025699,3205598
%N A176874 Minimal nonnegative integer that cannot be represented as
the sum of an m-gonal and a k-gonal numbers for any k,m less than n.
%C A176874 Indices of records in A176873 (with repetitions).
%C A176874 a(19)>10^7.
%H A176874 Max Alekseyev, <a
href="http://list.seqfan.eu/pipermail/seqfan/2010-April/004480.html">Proof
of the sequence A176874 infiniteness</a>. SeqFan maillist, Apr
26 2010.
%F A176874 a(n) = smallest integer s such that A176873(s)>=n.
%Y A176874 Cf. A176873, A176774
%K A176874 hard,more,nonn
%O A176874 3,2
%A A176874 Vladimir Shevelev and Max Alekseyev (maxale(AT)gmail.com),
Apr 27 2010

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