A188764 Primes p such that all prime factors of p-2 have exponent 3.

3, 29, 127, 24391, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 5177719, 9129331, 9938377, 10503461, 12326393, 15438251, 18191449, 24642173, 26730901, 28372627, 30080233, 39651823

Offset

1,1

Comments

A048636 is the subsequence of terms where there is only one prime divisor of p-2. - M. F. Hasler, Jan 13 2025

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) >> n^3. - Charles R Greathouse IV, Jan 14 2025

Example

30080233-2 = 311^3, 39651823-2 = 11^3*31^3, ...
3-2 = 1 has no prime factors, so is trivially a member.

Mathematica

Prepend[Select[Table[Prime[n], {n, 3000000}], Length[Union[Last/@FactorInteger[#-2]]]==1&&Union[Last/@FactorInteger[#-2]]=={3}&], 3]
Prepend[Select[Prime[Range[25*10^5]], Union[FactorInteger[#-2][[All, 2]]]=={3}&], 3] (* Harvey P. Dale, Nov 22 2018 *)
seq[lim_] := Select[Select[Range[Floor[Surd[lim-2, 3]]], SquareFreeQ]^3 + 2, PrimeQ]; seq[4*10^7] (* Amiram Eldar, Jan 18 2025 *)

Prog

(PARI) list(lim)=my(v=List()); forsquarefree(k=1, sqrtnint(lim\1-2, 3), my(p=k[1]^3+2); if(isprime(p), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Jan 14 2025

Crossrefs

Subsequence of A144953; A048636 is a subsequence.

Cf. A089195, A188717.

Sequence in context: A094068 A084105 A024386 * A171355 A163854 A227046

Adjacent sequences: A188761 A188762 A188763 * A188765 A188766 A188767

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2011

Extensions

a(1) = 3 inserted by Charles R Greathouse IV, Jan 14 2025

Status

approved