cp's OEIS Frontend

A121307 Products of three primes of the form 3n-1 (A003627), not necessarily distinct.

%I A121307 #22 Jun 13 2024 14:57:56
%S A121307 8,20,44,50,68,92,110,116,125,164,170,188,212,230,236,242,275,284,290,
%T A121307 332,356,374,404,410,425,428,452,470,506,524,530,548,575,578,590,596,
%U A121307 605,638,668,692,710,716,725,764,782,788,830,890,902,908,932,935,956
%N A121307 Products of three primes of the form 3n-1 (A003627), not necessarily distinct.
%C A121307 It would be incorrect to call these Eisenstein 3-almost primes. For the Eisenstein primes see A055664. - _N. J. A. Sloane_, Feb 06 2008.
%D A121307 J. H. Conway and R. K. Guy, The Book of Numbers. New York: Springer-Verlag, pp. 220-223, 1996.
%D A121307 Stan Wagon, "Eisenstein Primes," Section 9.8 in Mathematica in Action. New York: W. H. Freeman, pp. 319-323, 1991.
%H A121307 Giovanni Resta, <a href="/A121307/b121307.txt">Table of n, a(n) for n = 1..10000</a>
%t A121307 ok[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f == 3 && Max@ Mod[1 + First /@ f, 3] == 0]; Select[Range@ 1000, ok] (* _Giovanni Resta_, Jun 12 2016 *)
%o A121307 (PARI) list(lim)=my(v=List(),u=v,t); forprime(p=2,lim\4, if(p%3==2, listput(u,p))); for(i=1,#u, for(j=i,#u, if(u[i]*u[j]^2>lim, break); for(k=j,#u, t=u[i]*u[j]*u[k]; if(t>lim, break); listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%o A121307 (Python)
%o A121307 from sympy import primerange
%o A121307 from itertools import combinations_with_replacement as mc
%o A121307 def aupto(limit):
%o A121307     terms = [p for p in primerange(2, limit//4+1) if p%3 == 2]
%o A121307     return sorted(set(a*b*c for a, b, c in mc(terms, 3) if a*b*c <= limit))
%o A121307 print(aupto(957)) # _Michael S. Branicky_, Aug 20 2021
%Y A121307 Cf. A003627, A112770.
%Y A121307 Intersection of A004612 and A014612.
%Y A121307 Subsequence of A373589, which in turn is a subsequence of A373597.
%Y A121307 Cf. also A055664.
%K A121307 easy,nonn
%O A121307 1,1
%A A121307 _Jonathan Vos Post_, Sep 05 2006
%E A121307 Definition corrected by _N. J. A. Sloane_, Feb 06 2008
%E A121307 a(37)-a(53) from _Giovanni Resta_, Jun 12 2016
%E A121307 Name edited by _Antti Karttunen_, Jun 13 2024