A127329 - OEIS

%I #33 Sep 19 2024 21:59:02

%S 15,21,33,39,51,57,69,87,93,111,123,129,141,159,177,183,201,213,219,

%T 237,249,267,291,303,309,321,327,339,381,393,411,417,447,453,471,489,

%U 501,519,537,543,573,579,591,597,633,669,681,687,699,717,723,753,771,789

%N Semiprimes equal to the sum of three primes in arithmetic progression.

%F Conjecture: a(n) = 3*A000040(n+2). - _Zak Seidov_, Jun 28 2015

%F Every member of the sequence is 3 times a prime; it is believed that every prime >= 5 arises in this way. This is related to Goldbach's conjecture: see comments to A078611. - _Robert Israel_ and _Michel Marcus_, Jun 28 2015

%e a(1) = 15 because 15 = 3 + 5 + 7;

%e a(2) = 21 because 21 = 3 + 7 + 11.

%o (Magma) [3*NthPrime(n+2): n in [1..60]]; // _Vincenzo Librandi_, Jun 28 2015, assuming the conjecture holds

%Y Cf. A000040, A001358, A078611.

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Mar 30 2007

%E Corrected (57 = 7+19+31, 87 = 5+29+53, etc. inserted) by _R. J. Mathar_, Apr 22 2010