A114845 Slowest growing sequence of semiprimes having the semiprime-pairwise-average property: for any i,j, (a(i)+a(j))/2 is semiprime.

4, 14, 38, 134, 254, 13238, 252254, 691958, 952814, 3316238, 30364918838, 210339665174

Offset

1,1

Comments

Semiprime analog of A113875.

No more terms < 2*10^10. - Zak Seidov, Sep 03 2009

Links

Table of n, a(n) for n=1..12.

Example

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.

Crossrefs

Cf. A001358, A113832, A113875, A115760.

Sequence in context: A111583 A124615 A317606 * A141755 A064463 A130423

Adjacent sequences: A114842 A114843 A114844 * A114846 A114847 A114848

Keyword

nonn,more

Author

Jonathan Vos Post, Feb 20 2006

Extensions

More terms from Zak Seidov, Feb 21 2006

Corrected and extended by Zak Seidov, Sep 03 2009

a(11)-a(12) from Amiram Eldar, Jun 27 2024

Status

approved