A133517 - OEIS

%I #10 May 07 2019 14:03:12

%S 1,4,12,6,4,18,4,2,4,10,2,2,4,14,10,4,22,38,2,28,14,12,4,22,24,4,14,

%T 24,2,10,14,4,16,12,10,2,12,30,10,16,48,18,10,20,30,42,2,14,4,26,18,

%U 10,2,10,4,4,16,12,2,34,24,58,30,4,38,6,14,14,10,12,36,6,2,24,68,4,6,26,10

%N Smallest k such that p(n)^3 - k is prime where p(n) is the n-th prime.

%H Harvey P. Dale, <a href="/A133517/b133517.txt">Table of n, a(n) for n = 1..1000</a>

%e p(4)=7, 7^3 = 343; for odd k and n > 1, p(n)^r - k is even and thus not prime, so we only need consider even k.

%e for k = 2: 343 - 2 = 341, which is 11 * 31 and not prime.

%e for k = 4: 343 - 4 = 339, which is 3 * 113, also not prime.

%e for k = 6: 343 - 6 = 337, which is prime, so 6 is the smallest number that can be subtracted from 343 to make another prime.

%e Hence a(4) = 6.

%t sk[n_]:=With[{c=Prime[n]^3},c-NextPrime[c,-1]]; Array[sk,80] (* _Harvey P. Dale_, May 07 2019 *)

%o (PARI) a(n) = {k = 0; while (! isprime(prime(n)^3 - k), k++); return (k);} \\_Michel Marcus_, Aug 02 2013

%Y Cf. A030078, A054271, A091666, A133518, A133519, A133520, A133521, A133522, (A001223).

%K easy,nonn

%O 1,2

%A _Carl R. White_, Sep 14 2007