A176945 Semiprimes s such that r=(s^2+1)/2 is also a semiprime.

21, 33, 55, 77, 87, 91, 111, 115, 119, 129, 155, 161, 185, 215, 235, 247, 249, 259, 267, 287, 291, 295, 301, 303, 305, 323, 339, 341, 355, 361, 365, 381, 417, 427, 453, 469, 481, 485, 501, 505, 511, 517, 527, 533, 537, 551, 573, 589, 591

Offset: 1

Author

Jonathan Vos Post, Dec 08 2010

Keywords

• nonn
• easy

Comments

Semiprimes which are a leg of an integral right triangle whose hypotenuse is also semiprime. This is to A048161 as semiprimes A001358 are to primes A000040. All terms must be odd (else r is not an integer).

Examples

			a(1) = 21 because 21 = 3*7 is semiprime, and (21^2+1)/2 = 221 = 13 * 17 is semiprime.
a(2) = 33 because 33 = 3 * 11 is semiprime, and (33^2+1)/2 = 545 = 5 * 109 is semiprime.
a(3) = 55 because 55 = 5 * 11 is semiprime, and (55^2+1)/2 = 1513 = 17 * 89 is semiprime.
		

Crossrefs

Cf. A001358, A048161.

Programs

PARI

is_A176945(n)={ bittest(n,0) & bigomega(n)==2 & bigomega(1+n^2\2)==2 }  \\ M. F. Hasler, Dec 08 2010

Formula

{s such that s = p_1 * q_1 for p_1, q_1 primes, and r=(s^2+1)/2 = p_2 * q_2 for p_2, q_2 primes}.