A340212 - OEIS

%I #14 Jan 01 2021 11:26:40

%S 2,6,6,2,2,6,6,24,12,24,20,12,12,28,12,24,66,20,24,6,6,6,14,36,2,14,

%T 20,8,18,12,54,6,38,102,10,120,42,28,42,38,8,20,2,18,10,12,2,6,6,114,

%U 32,36,4,24,12,120,36,14,32,18,8,74,20,54,30,90,36,6,6,54,30,40,6,6,24,26,32,8,12,12

%N a(n) is the least k > 0 such that k*prime(n)+prime(n-1) and k*prime(n)+prime(n+1) are both prime.

%C All terms are even.

%C a(n) = 2 if and only if prime(n) is in A125146.

%H Robert Israel, <a href="/A340212/b340212.txt">Table of n, a(n) for n = 3..10000</a>

%e For n=3, prime(2)=3, prime(3)=5, prime(4)=7, and 2*5+3=13 and 2*5+7=17 are prime, so a(3)=2.

%p f:= proc(n) local p, q, r, k;

%p   p:= ithprime(n);

%p   q:= ithprime(n-1);

%p   r:= ithprime(n+1);

%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 map(f, [$3..100]);

%o (PARI) a(n) =  my(p=prime(n), k=1); while (! (isprime(k*p+precprime(p-1)) && isprime(k*p+nextprime(p+1))), k++); k; \\ _Michel Marcus_, Jan 01 2021

%Y Cf. A125146, A340210, A340214.

%K nonn

%O 3,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 31 2020