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

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2011

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Subsequence of A144953; A048636 is a subsequence.

Cf. A089195, A188717.

Programs

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 *)

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

Formula

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

Extensions

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