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Smallest primes such that when primes up to and including the n-th term in this sequence are summed, the result will be divisible by 10^n.
2

%I #5 Oct 06 2021 12:34:31

%S 5,23,35677,106853,632501,31190879,58369153,707712517,26219976521,

%T 87424229843,1642257355619,2962734127453

%N Smallest primes such that when primes up to and including the n-th term in this sequence are summed, the result will be divisible by 10^n.

%C In the long term, the prime sums' residues modulo 10^n are uniformly distributed, so one would expect the n-th term to be about the same size as the n-th prime.

%e 2+3+5 = 10, so 5 is the 1st term.

%e 2+3+5+7+11+13+17+19+23 = 100, so 23 is the 2nd term.

%K base,nonn,more

%O 1,1

%A _Phil Carmody_, Mar 07 2010