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A157473
Primes p such that (p-2)^(1/3) -+ 2 are also primes.
0
2, 127, 91127, 328511, 1157627, 2146691, 12326393, 125751503, 693154127, 751089431, 1033364333, 2102071043, 2222447627, 2893640627, 3314613773, 3951805943, 6591796877, 9063964127, 13464285941, 16406426423, 19880486831
OFFSET
1,1
EXAMPLE
(127-2)^(1/3) - 2 = 3 and (127-2)^(1/3) + 2 = 7, so 127 is in the sequence.
MATHEMATICA
q=2; lst={}; Do[p=Prime[n]; r=(p-q)^(1/3)-q; u=(p-q)^(1/3)+q; If[PrimeQ[r]&&PrimeQ[u], AppendTo[lst, p]], {n, 4*9!}]; lst
lst = {}; p = 0; While[p < 2955, If[ PrimeQ[p - 2] && PrimeQ[p + 2] && PrimeQ[p^3 + 2], AppendTo[lst, p^3 + 2]]; p++ ]; lst (* Robert G. Wilson v, Mar 08 2009 *)
Select[Prime[Range[10^6]], AllTrue[Surd[#-2, 3]+{2, -2}, PrimeQ]&] (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Aug 31 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(8)-a(21) from Robert G. Wilson v, Mar 08 2009
STATUS
approved