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A133520 Smallest k such that p(n)^4 + k is prime where p(n) is the n-th prime. 8

%I

%S 1,2,6,10,12,10,16,16,6,12,18,16,12,28,6,22,6,16,6,16,6,16,30,6,16,42,

%T 22,42,28,52,22,16,28,10,28,70,30,42,78,36,12,42,6,12,40,12,12,16,16,

%U 16,18,10,6,22,60,46,76,46,18,126,12,22,22,6,16,16,22,18,120,22,12,6,6,36

%N Smallest k such that p(n)^4 + k is prime where p(n) is the n-th prime.

%H Harvey P. Dale, <a href="/A133520/b133520.txt">Table of n, a(n) for n = 1..1000</a>

%e p(2)=3, 3^4 = 81; 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: 81 + 2 = 83, which is prime, so 2 is the smallest number that can be added to 81 to make a new prime.

%e Hence a(2) = 2.

%t NextPrime[#]-#&/@(Prime[Range[80]]^4) (* _Harvey P. Dale_, May 17 2015 *)

%Y Cf. A030814, A054271, A091666, A133517, A133518, A133519, A133521, A133522, (A001223).

%K easy,nonn

%O 1,2

%A _Carl R. White_, Sep 14 2007

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Last modified September 24 06:24 EDT 2020. Contains 337317 sequences. (Running on oeis4.)