what is the next term of 1,3,20 ?

[T. D. Noe]

At 4:02 PM -0500 4/19/05, Eric W. Weisstein wrote:
>On Tue, 19 Apr 2005, Emeric Deutsch wrote:
>
>> Dear seqfans,
>> I know you need more information. Here is the full
>> description:
>>
>> values of n such that the n-th prime is a divisor of the sum
>> of the first n primes.
>>
>> 1 because 2 (the 1st prime) is a divisor of 2;
>> 3 because 5 (the 3rd prime) is a divisor of 2+3+5=10;
>> 20 because 71 (the 20th prime) is a divisor of 2+3+5+...+71=639.
>>
>> A fresher question: what are the next terms?
>
>1, 3, 20, 31464, ...
>
>No others < 10^7.

The next term is then the 22,096,548th prime, which is 415,074,643.
Checked all primes < 10^9.

Tony