A105936 Numbers that are the product of exactly 3 primes and are of the form prime(n) + prime(n+1).

8, 12, 18, 30, 42, 52, 68, 78, 138, 172, 186, 222, 258, 268, 410, 434, 508, 548, 618, 668, 762, 772, 786, 892, 906, 946, 978, 1002, 1030, 1132, 1334, 1374, 1446, 1542, 1606, 1758, 1866, 1878, 1948, 2006, 2022, 2252, 2334, 2414, 2452, 2468, 2486, 2572, 2588

Offset: 1

Author

Giovanni Teofilatto, Apr 27 2005

Keywords

• easy
• nonn

Comments

Minimal triprimes (A014612) of the form prime(n) + prime(n+1).

Intersection of A001043 and A014612:

a(1) = A001043(2) = A014612(1),

a(2) = A001043(2) = A014612(2). - Zak Seidov, Jan 31 2017

Examples

			a(2) = 12 because 12 = 5 + 7 = 3*2^2;
a(3) = 18 because 18 = 7 + 11 = 2*3^2.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Almost Prime.

Crossrefs

Cf. A001043, A014612.

Programs

Mathematica

Select[Range[8,10000,2], 3 == PrimeOmega[#] && NextPrime[#/2] + NextPrime[#/2, -1] == # &] (* Zak Seidov, Jan 31 2017 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim\2, forprime(q=2,min(p,lim\p\2), my(t=2*p*q); if(precprime(p*q)+nextprime(p*q)==t, listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

Formula

a(n) is equal to the product of 3 primes if the arithmetic mean of prime(n) and prime(n+1) is a semiprime.

Extensions

More terms from Reinhard Zumkeller, May 03 2005