A242218 Semiprimes which are the arithmetic mean of three consecutive primes.

511, 537, 1073, 1461, 1501, 1541, 1763, 2071, 2181, 2449, 4101, 4387, 4399, 4467, 4559, 4607, 4681, 4705, 5089, 5257, 5429, 6415, 6621, 6671, 7097, 7111, 7261, 7391, 7447, 7811, 7831, 7897, 7909, 7969, 8079, 8129, 8193, 8333, 8639, 8915, 9101, 9113, 9123, 9211

Offset: 1

Author

K. D. Bajpai, May 07 2014

Keywords

• nonn

Examples

			a(1) = 511 = (503 + 509 + 521)/3 = 7 * 73 is semiprime.
a(2) = 537 = (523 + 541 + 547)/3 = 3 * 179 is semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A133529, A216432, A234297.

Programs

Maple

with(numtheory): A242218:= proc()local k ; k:=(ithprime(x)+ithprime(x+1)+ithprime(x+2))/3; if k=floor(k) and bigomega(k)=2 then RETURN (k);  fi; end: seq(A242218 (),x=2..2000);

PARI

for(k=1, 2000, t=prime(k)+prime(k+1)+prime(k+2); if(t%3==0 && bigomega(t/3)==2, print1(t/3, ", "))) \\ Colin Barker, May 08 2014