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

%I #14 Jun 27 2024 01:34:19

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

%T 210339665174

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

%C Semiprime analog of A113875.

%C No more terms < 2*10^10. - _Zak Seidov_, Sep 03 2009

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

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

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

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

%e 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.

%Y Cf. A001358, A113832, A113875, A115760.

%K nonn,more

%O 1,1

%A _Jonathan Vos Post_, Feb 20 2006

%E More terms from _Zak Seidov_, Feb 21 2006

%E Corrected and extended by _Zak Seidov_, Sep 03 2009

%E a(11)-a(12) from _Amiram Eldar_, Jun 27 2024