A157473 Primes p such that (p-2)^(1/3) -+ 2 are also primes.

2, 127, 91127, 328511, 1157627, 2146691, 12326393, 125751503, 693154127, 751089431, 1033364333, 2102071043, 2222447627, 2893640627, 3314613773, 3951805943, 6591796877, 9063964127, 13464285941, 16406426423, 19880486831

Offset

1,1

Links

Table of n, a(n) for n=1..21.

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

Cf. A127435, A127436, A157467, A157468.

Sequence in context: A092832 A181001 A105761 * A004864 A106319 A338932

Adjacent sequences: A157470 A157471 A157472 * A157474 A157475 A157476

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Extensions

a(8)-a(21) from Robert G. Wilson v, Mar 08 2009

Status

approved