Extend New Binary Sequence ?

[Jonathan Post]

A bit over 2 years ago, between my father's funeral and wake, I
distracted myself by computing with a 4-banger pocket calculator
several related seqs, which I don't recall if I submitted to OEIS or
seqfans.

a(n) = a(n-1) + a([n/3])

a(n) = a(n-1) + a([n/4])

a(n) = a([(n-1)/3]) + a([2n/3])

a(n) = a(n-1) + a([n/e])

a(n) = a(n-1) + a([n/pi])

a(n) = a(n-1) + a([sqrt(n)])

a(n) = a(n-1) + a([log(n)])

a(n) = a([n-1)/3]) + a([2*(n-2)/3) + a(n-3)

and some others.  Hand-written results, on back of funeral paperwork,
hard for me to dig out of my million-page physical paperwork archive.

Are any of these in OEIS, and are any of interest?

My father had only 1 math "publication" in his life, albeit he got
math credit to graduate Harvard by having taught trig and maybe
spherical trig to navigators when he was a World War II Army flight
instructor.  He had a letter to the editor of a Rhode Island newspaper
(where he'd retired) arguing that 1 was prime. Until somewhat berfore
1899, that was considered correct to some professionals...