[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
robert.gerbicz at gmail.com
Mon Jun 22 01:10:22 CEST 2009
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.
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