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%I #19 May 31 2022 06:48:58
%S 2,2,5,197,7,157,29,41,2,599,3,13,293,19,181,59,7,1489,557,43,11,23,2,
%T 227,191,349,179,2,103,5479,2,7,131,971,37,2,6917,23,1279,10903,593,
%U 311,239,2711,6277,1669,257,293,503,1861,13613,11,569,719,619,709,4523,3,3,2549,1361,383,3,10193
%N a(n) is the least prime p such that the numerator of the sum of reciprocals of the 2*n+1 consecutive primes starting with p is a prime.
%C We use 2*n+1 consecutive primes rather than n because the numerator of the sum of reciprocals of an even number of odd primes is even.
%C The numerators are in A354221.
%H Robert Israel, <a href="/A353534/b353534.txt">Table of n, a(n) for n = 1..330</a>
%e a(3) = 5 because the sum of reciprocals of 2*3 + 1 = 7 primes starting with 5 is 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 = 24749279/37182145, and 24749279 is prime.
%p f:= proc(n) local i,k,v;
%p for k from 1 do
%p v:= numer(add(1/ithprime(i),i=k..k+2*n));
%p if isprime(v) then return ithprime(k) fi
%p od
%p end proc:
%p map(f, [$1..70]);
%Y Cf. A024451, A244622, A354221.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, May 29 2022
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