Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Jan 14 2025 15:25:44
%S 3,29,127,24391,274627,328511,357913,571789,1157627,1442899,1860869,
%T 2146691,2924209,5177719,9129331,9938377,10503461,12326393,15438251,
%U 18191449,24642173,26730901,28372627,30080233,39651823
%N Primes p such that all prime factors of p-2 have exponent 3.
%C A048636 is the subsequence of terms where there is only one prime divisor of p-2. - _M. F. Hasler_, Jan 13 2025
%H Charles R Greathouse IV, <a href="/A188764/b188764.txt">Table of n, a(n) for n = 1..10000</a>
%H Charles R Greathouse IV, <a href="/A188764/b188764_1.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) >> n^3. - _Charles R Greathouse IV_, Jan 14 2025
%e 30080233-2=311^3, 39651823-2=11^3*31^3,...
%e 3-2 = 1 has no prime factors, so is trivially a member.
%t Select[Table[Prime[n],{n,3000000}],Length[Union[Last/@FactorInteger[#-2]]]==1&&Union[Last/@FactorInteger[#-2]]=={3}&]
%t Select[Prime[Range[25*10^5]],Union[FactorInteger[#-2][[All,2]]]=={3}&] (* _Harvey P. Dale_, Nov 22 2018 *)
%o (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
%Y Subsequence of A144953; A048636 is a subsequence.
%Y Cf. A089195, A188717.
%K nonn,changed
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 09 2011