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%I #7 Feb 16 2023 10:11:00
%S 2977,5357,10537,15697,15829,21949,22417,23257,30017,33509,33949,
%T 37909,38509,46033,51073,52333,58813,59317,63937,68617,68797,78409,
%U 84877,85273,92513,94177,97229,98233,100873,114977,115697,118177,124229,131977,137257,145217,148637,153973,154549,156193,159253
%N Semiprimes k such that k+4, k+6, k+9, k+10 and k+14 are also semiprimes.
%C 4, 6, 9, 10, 14 are the first five semiprimes.
%C The sixth semiprime is 15, but there are no semiprimes k such that k+4, k+9, k+10, k+14 and k+15 are all semiprimes, because at least one of k, k+4, k+9, k+10, k+14 and k+15 is divisible by 4, and 4 is the only semiprime divisible by 4.
%C All terms == 1, 25 or 29 (mod 36).
%H Robert Israel, <a href="/A360666/b360666.txt">Table of n, a(n) for n = 1..9340</a>
%e a(3) = 10537 is a term because
%e 10537 = 41 * 257
%e 10537 + 4 = 10541 = 83 * 127
%e 10537 + 6 = 10543 = 13 * 811
%e 10537 + 9 = 10546 = 2 * 5273
%e 10537 + 10 = 10547 = 53 * 199
%e 10537 + 14 = 10551 = 3 * 3517
%e are all semiprimes.
%p select(t -> isprime((t+9)/2) and numtheory:-bigomega(t) = 2 and numtheory:-bigomega(t+4) = 2 and numtheory:-bigomega(t+6) = 2 and numtheory:-bigomega(t+10) = 2 and numtheory:-bigomega(t+14) = 2, [seq(seq(36*i+j, j=[1,25,29]),i=0..10^5)]);
%Y Cf. A001358.
%K nonn
%O 1,1
%A _Zak Seidov_ and _Robert Israel_, Feb 15 2023