This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A132282 #25 Nov 04 2018 01:33:38
%S A132282 2,3,29,127,24391,357913,571789,1442899,5177719,18191449,30080233,
%T A132282 73560061,80062993,118370773,127263529,131872231,318611989,344472103,
%U A132282 440711083,461889919,590589721,756058033,865523179,1095912793
%N A132282 Near-cube primes: primes of the form p^3 + 2, where p is noncomposite.
%C A132282 The corresponding near-cube prime indices q are A132281. Analog of near-square primes. After a(1) = 2, all values must be odd. Numbers of the form n^2+2 for n=1, 2, ... are 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, ... (A059100). These are prime for indices n = 1, 3, 9, 15, 21, 33, 39, 45, 57, 81, 99, ... (A067201), corresponding to the near-square primes 3, 11, 83, 227, 443, 1091, 1523, 2027, ... (A056899). Helfgott proves with minor conditions that: "Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is squarefree." Note that 47^3 + 2 = 103825 = 5^2 * 4153 and similarly 97^3 + 2 is divisible by 5^2, but otherwise an infinite number of p^3+2 are squarefree.
%H A132282 Harald Andres Helfgott, <a href="http://arXiv.org/abs/0706.1497">Power-free values, repulsion between points, differing beliefs and the existence of error</a>, arXiv:0706.1497 [math.NT], 2007.
%F A132282 a(n) = A132281(n)^3 + 2. {p in A000040 such that for some q = 0, 1, or q in A000040, we have p = A067200(q) = A084380(q) = q^3 + 2 is in A000040}.
%F A132282 a(n) = A048636(n-2) for n >= 3. - _Georg Fischer_, Nov 03 2018
%e A132282 a(1) = 0^3 + 2 = 2 is prime and 0 is noncomposite.
%e A132282 a(2) = 1^3 + 2 = 3 is prime and 1 is noncomposite.
%e A132282 a(3) = 3^3 + 2 = 29 is prime and 3 is prime.
%e A132282 a(4) = 5^3 + 2 = 127 is prime and 5 is prime.
%e A132282 a(5) = 29^3 + 2 = 24391 is prime and 29 is prime.
%e A132282 45^3 + 2 = 91127 is prime, but not in this sequence because 45 is not prime.
%e A132282 63^3 + 2 = 250049 is prime, but not in this sequence because 63 is not prime.
%e A132282 a(6) = 71^3 + 2 = 357913 is prime.
%e A132282 a(7) = 83^3 + 2 = 571789 is prime.
%e A132282 a(8) = 113^3 + 2 = 1442899 is prime.
%t A132282 Join[{2, 5}, Select[Prime[Range[200]]^3 + 2, PrimeQ[ # ] &]] (* _Stefan Steinerberger_, Aug 17 2007 *)
%o A132282 (PARI) v=[2,3]; forprime(p=3, 1e4, if(isprime(t=p^3+2), v=concat(v, t))); t \\ _Charles R Greathouse IV_, Feb 14 2011
%Y A132282 Cf. A000040, A048636, A056899, A059100, A067200, A067201, A084380, A132281.
%K A132282 easy,nonn
%O A132282 1,1
%A A132282 _Jonathan Vos Post_, Aug 16 2007
%E A132282 More terms from _Stefan Steinerberger_, Aug 17 2007
%E A132282 a(2) corrected by _Charles R Greathouse IV_, Feb 14 2011