cp's OEIS Frontend

A262723 Products of three distinct primes that form an arithmetic progression.

%I A262723 #17 Aug 27 2022 08:10:03
%S A262723 105,231,627,897,935,1581,1729,2465,2967,4123,4301,4715,5487,7685,
%T A262723 7881,9717,10707,11339,14993,16377,17353,20213,20915,23779,25327,
%U A262723 26331,26765,29341,29607,32021,33335,40587,40807,42911,48635,49321,54739,55581,55637,59563,60297,63017
%N A262723 Products of three distinct primes that form an arithmetic progression.
%C A262723 This sequence is subsequence of A046389, A088595, A187073, A203614 and A229094.
%C A262723 Obviously, the most repeated prime divisor for values of a(n) is 3. - _Altug Alkan_, Sep 30 2015
%C A262723 These are numbers 3(2k + 3)(4k + 3) where 2k + 3 and 4k + 3 are prime, together with numbers p(p - 6d)(p + 6d) where p, p - 6d, and p + 6d are prime. - _Charles R Greathouse IV_, Mar 16 2018
%H A262723 Charles R Greathouse IV, <a href="/A262723/b262723.txt">Table of n, a(n) for n = 1..10000</a>
%e A262723 627 is in this sequence because 627=3*11*19, and 3, 11, 19 form an arithmetic progression (11-3 = 19-11).
%t A262723 Select[Range@ 64000, And[SquareFreeQ@ #, PrimeOmega@ # == 3, Subtract @@ Differences[First /@ FactorInteger@ #] == 0] &] (* _Michael De Vlieger_, Sep 30 2015 *)
%o A262723 (PARI) for(i=2,10^5,if(issquarefree(i)&&omega(i)==3,f=factor(i);if(f[1, 1]+f[3, 1]==2*f[2,1],print1(i,", "))))
%o A262723 (PARI) list(lim)=my(v=List()); lim\=1; forstep(d=6,sqrtint(lim\10),6, forprime(p=d+5, solve(x=sqrtn(lim,3),d*sqrtn(lim,3), x^3-d^2*x-lim)+.5, if(isprime(p-d) && isprime(p+d), listput(v, p*(p-d)*(p+d))))); forprime(p=5,(sqrt(24*lim+81)-27)/12+3.5, if(isprime(2*p-3), listput(v,p*(2*p-3)*3))); Set(v) \\ _Charles R Greathouse IV_, Mar 16 2018
%Y A262723 Cf. A046389, A088595, A187073, A203614, A229094.
%K A262723 nonn
%O A262723 1,1
%A A262723 _Antonio Roldán_, Sep 28 2015
%E A262723 New name from _Peter Munn_, Aug 27 2022