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A114845
Slowest growing sequence of semiprimes having the semiprime-pairwise-average property: for any i,j, (a(i)+a(j))/2 is semiprime.
1
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
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
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