A396687 - OEIS

%I #15 Jun 07 2026 22:44:23

%S 1,2,2,2,2,4,2,3,3,1,3,6,2,1,2,4,1,3,2,4,6,4,6,2,2,2,7,6,4,2,5,3,3,2,

%T 1,7,6,1,2,4,8,6,6,9,1,10,4,8,2,3,6,2,1,1,2,8,1,3,11,5,2,7,6,6,2,5,5,

%U 3,2,6,5,1,5,7,5,4,3,2,4,2,2,4,3,5,4,14

%N Smallest k > 0 such that 2*prime(n) - prime(n-k) is prime.

%H Ruud H.G. van Tol, <a href="/A396687/b396687.txt">Table of n, a(n) for n = 3..10000</a>

%F A078611(n) = prime(n) - prime(n - a(n)).

%e a(3) = 1, because prime(3) = 5 and prime(3 - a(3)) = prime(2) = 3 and 5 + (5 - 3) = 7 is prime.

%e a(14) = 6, because 6 is the smallest k > 0 for which 2 * prime(14) - prime(14 - k) is prime.

%t a[n_]:=Module[{k=1},While[!PrimeQ[2Prime[n]-Prime[n-k]], k++]; k]; Array[a,86,3] (* _Stefano Spezia_, Jun 02 2026 *)

%o (PARI) a(n)= if(n<3, 0, my(p=prime(n), k=0); until(isprime(p*2-prime(n-k++)), ); k)

%o (PARI) a(n) = {my(p = prime(n), ptwice = 2*p, other); forprime(q = p+1, ptwice-1, if(isprime(ptwice - q), other = ptwice - q; break)); n-primepi(other)} \\ _David A. Corneth_, Jun 02 2026

%Y Cf. A000040, A078611, A179835.

%K easy,nonn

%O 3,2

%A _Ruud H.G. van Tol_, Jun 02 2026