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A329727
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Numbers k such that k^3 +- 2 and k +- 2 are prime.
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2
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129, 1491, 1875, 2709, 5655, 6969, 10335, 14325, 14421, 17319, 26559, 35109, 37509, 43719, 50229, 52629, 101871, 102795, 104325, 105501, 120429, 127599, 132699, 136395, 137829, 157521, 172425, 173685, 179481, 186189, 191829, 211371, 219681, 221199, 229215, 234195
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OFFSET
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1,1
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COMMENTS
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All terms in this sequence are divisible by 3.
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LINKS
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Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
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EXAMPLE
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a(1) = 129:
129^3 + 2 = 2146691;
129^3 - 2 = 2146687;
129 + 2 = 131;
129 - 2 = 127; all four results are prime.
a(2) = 1491:
1491^3 + 2 = 3314613773;
1491^3 - 2 = 3314613769;
1491 + 2 = 1493;
1491 - 2 = 1489; all four results are prime.
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MATHEMATICA
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Select[Range[500000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[# + 2] && PrimeQ[# - 2] &]
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PROG
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(Magma) [k:k in [1..250000]|forall{m:m in [-2, 2]|IsPrime(k+m) and IsPrime(k^3+m)}]; // Marius A. Burtea, Nov 20 2019
(PARI) isok(k) = isprime(k-2) && isprime(k+2) && isprime(k^3-2) && isprime(k^3+2); \\ Michel Marcus, Nov 24 2019
(PARI) list(lim)=my(v=List(), p=127, k); forprime(q=131, lim+2, if(q-p==4 && isprime((k=p+2)^3-2) && isprime(k^3+2), listput(v, k)); p=q); Vec(v) \\ Charles R Greathouse IV, May 06 2020
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CROSSREFS
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Intersection of A038599, A067200, and A087679.
Cf. A040976, A052147, A090121, A268043, A268186.
Sequence in context: A046286 A341552 A251095 * A209532 A233305 A268266
Adjacent sequences: A329724 A329725 A329726 * A329728 A329729 A329730
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KEYWORD
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nonn
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AUTHOR
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K. D. Bajpai, Nov 19 2019
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STATUS
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approved
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