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

105, 231, 627, 897, 935, 1581, 1729, 2465, 2967, 4123, 4301, 4715, 5487, 7685, 7881, 9717, 10707, 11339, 14993, 16377, 17353, 20213, 20915, 23779, 25327, 26331, 26765, 29341, 29607, 32021, 33335, 40587, 40807, 42911, 48635, 49321, 54739, 55581, 55637, 59563, 60297, 63017

Offset

1,1

Comments

This sequence is subsequence of A046389, A088595, A187073, A203614 and A229094.

Obviously, the most repeated prime divisor for values of a(n) is 3. - Altug Alkan, Sep 30 2015

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

Links

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

Example

627 is in this sequence because 627=3*11*19, and 3, 11, 19 form an arithmetic progression (11-3 = 19-11).

Mathematica

Select[Range@ 64000, And[SquareFreeQ@ #, PrimeOmega@ # == 3, Subtract @@ Differences[First /@ FactorInteger@ #] == 0] &] (* Michael De Vlieger, Sep 30 2015 *)

Prog

(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, ", "))))
(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

Crossrefs

Cf. A046389, A088595, A187073, A203614, A229094.

Sequence in context: A308643 A229094 A307108 * A250757 A350199 A146257

Adjacent sequences: A262720 A262721 A262722 * A262724 A262725 A262726

Keyword

nonn

Author

Antonio Roldán, Sep 28 2015

Extensions

New name from Peter Munn, Aug 27 2022

Status

approved