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

8, 20, 44, 50, 68, 92, 110, 116, 125, 164, 170, 188, 212, 230, 236, 242, 275, 284, 290, 332, 356, 374, 404, 410, 425, 428, 452, 470, 506, 524, 530, 548, 575, 578, 590, 596, 605, 638, 668, 692, 710, 716, 725, 764, 782, 788, 830, 890, 902, 908, 932, 935, 956

Offset: 1

Author

Jonathan Vos Post, Sep 05 2006

Keywords

• easy
• nonn

Comments

It would be incorrect to call these Eisenstein 3-almost primes. For the Eisenstein primes see A055664. - N. J. A. Sloane, Feb 06 2008.

References

• J. H. Conway and R. K. Guy, The Book of Numbers. New York: Springer-Verlag, pp. 220-223, 1996.
• Stan Wagon, "Eisenstein Primes," Section 9.8 in Mathematica in Action. New York: W. H. Freeman, pp. 319-323, 1991.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003627, A112770.

Intersection of A004612 and A014612.

Subsequence of A373589, which in turn is a subsequence of A373597.

Cf. also A055664.

Programs

Mathematica

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 *)

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

Python

from sympy import primerange
from itertools import combinations_with_replacement as mc
def aupto(limit):
    terms = [p for p in primerange(2, limit//4+1) if p%3 == 2]
    return sorted(set(a*b*c for a, b, c in mc(terms, 3) if a*b*c <= limit))
print(aupto(957)) # Michael S. Branicky, Aug 20 2021

Extensions

Definition corrected by N. J. A. Sloane, Feb 06 2008

a(37)-a(53) from Giovanni Resta, Jun 12 2016

Name edited by Antti Karttunen, Jun 13 2024