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Numbers n such that n and n^4 are sums of two twin primes.
1

%I #21 Feb 01 2017 11:42:25

%S 384,840,8676,33300,34980,37044,39984,42024,50604,53760,55056,61680,

%T 64380,71064,83520,88176,97644,103740,120204,129840,133896,148764,

%U 154524,160416,168120,173064,184800,188880,199056,207984,234744,266640,292116,307044,356184

%N Numbers n such that n and n^4 are sums of two twin primes.

%C All terms are multiples of 12.

%H Harvey P. Dale, <a href="/A212430/b212430.txt">Table of n, a(n) for n = 1..1000</a>

%F n/2 +/-1 and (n^4)/2 +/- 1 are primes.

%e 384=191+193, 384^3=147456=73727+73729.

%t Select[12 Range[30000],AllTrue[{#/2+1,#/2-1,#^4/2+1,#^4/2-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 01 2017 *)

%o (PARI) isok(n) = !(n % 2) && isprime(n/2-1) && isprime(n/2+1) && isprime(n^4/2-1) && isprime(n^4/2+1); \\ _Michel Marcus_, Oct 19 2013

%Y Cf. A001043, A074924, A213784, A213789, A213811.

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 21 2012