[seqfan] Re: Sums of values of A113907. Sums of dimensions of the five sporadic Lie groups. Dimensions of direct products of sporadic Lie groups.

[Robert Gerbicz]

2009/6/22 Jonathan Post <jvospost3 at gmail.com>

> 14, 28, 42, 52, 56, 66, 70, 78, 80, 84, 92, 94, 98, 104, 106, 108,
> 112, 118, 120, 122, 126, 130, 132, 133, 134, 136, 140, 144, 146, 148,
> 150, 154, 156, 158, 160, 161, 162, 164
>
> Sorry if I've made some errors doing this by hand. Am I getting
> anything right here, in arithmetic and interpretation?
>
> Sums of values of A113907.  Sums of dimensions of the five sporadic
> Lie groups. Dimensions of direct products of sporadic Lie groups.
> Integers of the form 14a + 52b + 78c + 133d + 248e for nonnegative
> integers a, b, c, d.
>
> The first value arising in two different ways is 156 = 52 + 52 + 52 = 78 +
> 78.
>
> The first triplets of three consecutive values: (132,133,134),
> (160,161,162).
>
> All sufficiently large integers are in this sequence.  What is the
> maximum value not in the sequence?
>
>
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Use the Frobenius problem: http://en.wikipedia.org/wiki/Coin_problem
since gcd(52,133)=1 the maximum value not in the sequence is
52*133-52-133=6731 even using only 52 and 133, by a simple dp code you can
check all values up to this limit and in fact n=327 is the maximum not in
the original sequence.