[seqfan] sequence without proof

[jnthn stdhr]

Hello all.

I have a program that reproduces A002569 <https://oeis.org/A002569>.
Unlike A002569, which uses the max() function to find the greatest value of
row n in A008284, my program starts with k = 1 and increments k by one when
T(b, k+1) > T(a,k), b > a.  I have no proof that it is correct for all n,
but it hasn't produced any errors for large values of n. By adding a print
statement that reports the value of n when k is incremented I get the
unknown sequence:

1, 4, 7, 10, 15, 18, 23, 29, 35, 40, 47, 54, 60, 68, 75, 83, 90, 99,...

I would like to enter this sequence into the database.  Should I include
"apparently" in the name?  Or perhaps just add a comment with
"apparently"?  Or can someone show a proof?

-Jonathan