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A353534 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.

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