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%I #17 Jan 01 2021 18:10:15
%S 1,2,6,18,6,48,12,2,36,8,6,30,66,12,22,66,18,96,18,8,30,6,24,60,114,
%T 114,138,30,66,12,18,42,54,120,14,6,48,38,22,180,78,6,30,18,14,24,6,
%U 18,12,6,36,12,2,66,4,240,18,12,60,150,78,84,90,126,42,18,36,30,12,36,24,14,24,6,6,84,48
%N a(n) is the least k > 0 such that k*prime(n)+prime(n+1) and k*prime(n)+prime(n+2) are both prime.
%C a(n) is even for n > 1.
%C a(n) = 2 for n in A340225.
%H Robert Israel, <a href="/A340210/b340210.txt">Table of n, a(n) for n = 1..10000</a>
%e For n=3, prime(3)=5, prime(4)=7, prime(5)=11, and 6*5+7= 37 and 6*5+11=41 are prime, so a(3)=6.
%p f:= proc(n) local p, q,r,k;
%p p:= ithprime(n);
%p q:= ithprime(n+1);
%p r:= ithprime(n+2);
%p for k from 2 by 2 do
%p if isprime(k*p+q) and isprime(k*p+r) then return k fi
%p od
%p end proc:
%p f(1):= 1:
%p map(f, [$1..100]);
%Y Cf. A340211, A340212, A340225.
%K nonn
%O 1,2
%A _J. M. Bergot_ and _Robert Israel_, Dec 31 2020
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