A340226 - OEIS

%I #9 Feb 23 2023 14:01:31

%S 2,4,4,6,6,4,42,18,6,6,10,10,6,2,120,18,12,6,6,30,6,24,70,6,18,60,6,

%T 66,52,30,6,42,18,366,2,6,6,2,18,18,12,40,30,6,2,78,66,36,66,6,42,54,

%U 2,2,36,90,60,36,18,48,6,6,46,42,90,24,4,6,126,6,60,2,150,156,30,144,30,48,30,100,4

%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.

%H Robert Israel, <a href="/A340226/b340226.txt">Table of n, a(n) for n = 3..10000</a>

%e For n = 4, 5, 7 and 11 are the third to fifth primes, 4*7-5 = 23 and 4*7-11 = 17 are prime, so a(4)=4.

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

%p   p:= ithprime(n);

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

%p   for k from 2 by 2 do if isprime(k*p-q) and isprime(k*p-r) then return k fi od;

%p end proc:

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

%t lkp[p_]:=Module[{a=NextPrime[p,-1],b=NextPrime[p],k=2},While[Total[Boole[ PrimeQ[ k p-{a,b}]]]!=2,k=k+2];k]; lkp/@Prime[Range[3,90]] (* _Harvey P. Dale_, Feb 23 2023 *)

%Y Cf. A340212.

%K nonn

%O 3,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 01 2021