1,1

Semiprime analogue of A113875 "slowest growing sequence of primes having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime."

The pairwise average of the semiprimes {4 = 2^2, 14 = 2*7} is {9 = 3^2}.

The pairwise averages of the semiprimes {4, 14, 38} are {9, 21, 26}.

The pairwise averages of the semiprimes {4, 14, 38, 134} are {9, 21, 26, 69, 74, 86}.

The pairwise averages of the semiprimes {4, 14, 38, 134, 254} are {9, 21, 26, 69, 74, 86, 129, 134, 146, 194}.

278 is not an element because, although (4 + 278)/2 = 141 = 3 * 47, and (14 + 278)/2 = 146 = 2 * 73, and (38 + 278)/2 = 158 = 2 * 79, and (134 + 278)/2 = 206 = 2 * 103, the pattern breaks down with (254 + 278)/2 = 266 = 2 * 7 * 19 is not semiprime. 758 also works with 4, 14, 38, and 134, but fails with 254. By exhaustive search, there is no a(6) < 1000.

Cf. A001358, A113832, A113875, A115760.

Sequence in context: A086954 A111583 A124615 this_sequence A064463 A130423 A055484

Adjacent sequences: A114842 A114843 A114844 this_sequence A114846 A114847 A114848

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 20 2006

More terms from Zak Seidov (zakseidov(AT)yahoo.com), Feb 21 2006