sequences in n- sumf(r)

[murthy amarnath]

Dear Neil and Seqfans,
I have submitted some sequences based on an idea which
can be extended further.

Largest prime in the sequence n- sum f(r) where
 sum f(r)= f(1) +f(2) ...f(r).
0 if no such prime exists.
Seq(1): e.g. f(r) = r(r+1)/2 = r'th triangular number.
a(30) = 3,
we have ----> 30, 29, 28, 25,21,16,10, and finally 3.
a(36) = 0. ---> 36,35,33,30,26,21,15,8,0.
I have conjectured that there are finitely many zeros
in this sequence (A090302).
Seq(2): f(r) = prime(r).
These two I have submitted.
Is the idea worth exploring for  f(r) = r^2, r^3,
phi(r), tau(r),sigma(r),Fibonacci number, composite
number, or any other meaningful function. 
And I conjecture that in most cases there exists a
number k such that for all n > k, a(n) is non zero.
thanks
regards
amarnath


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