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

[Jonathan Post]

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?