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%I #27 Feb 16 2019 07:08:04
%S 1,3,9,25,68,191,547,1593,4692,13941,41710,125494,379324,1150976,
%T 3503793,10695889,32729282,100361004,308313172,948694980,2923428287,
%U 9020381557,27865631947,86174159206,266752375679,826469488966,2562720437746
%N a(n) is the smallest k such that the sum of the first k primes is >= 10^n.
%C The final primes in the sums are 2, 5, 23, 97, 337, 1153, 3943, 13441, 45197, 151091, 502259, 1662377, 5477083, 17993477, 58954411, 192682537, 628420129, 2045812157, 6649205951, 21579536893, 69943284097, 226431374423, 732253012171, 2365707119579, 7636102747789, 24627776205037, 79368662592367, 255604186937213, 822628809813047, ..., .
%t p = 2; k = s = 0; lst = {}; Do[ While[s < 10^n, s = s + p; p = NextPrime@ p; k++]; AppendTo[lst, k; Print@ k], {n, 20}]; lst
%Y Cf. A007504, A323360, A323361.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Jan 12 2019
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