Pairs and triple semiprimes

all at abouthugo.de all at abouthugo.de
Fri Apr 4 23:36:01 CEST 2003


SeqFans,

I was a little bit surprised that I could not find
the following sequences in the OEIS, so I submitted (compiled by hand,
so please check):

%I A082130 
%S A082130 17 25 28 43 46 47 60 61 71 72 80 92 93 101 102 107 108 109
110 
118 124 133 144 145 150 151 152 160 161 164 170 196 197 206 
207 208 223 226 235 236 258 259 
%N A082130 2*n-1 and 2*n+1 are semiprimes. 
%e A082130 a(1)=17 because 2*17-1=33=3*11 and 2*17+1=35=5*7 are both
semiprimes. 
%Y A082130 Cf. A001358, A082131 
%O A082130 1 
%K A082130 ,nonn, 
%A A082130 Hugo Pfoertner (hugo at pfoertner.org), Apr 04 2003

%I A082131 
%S A082131 93 121 143 185 203 215 217 219 289 301 303 321 393 
413 415 471 517 535 581 669 687 697 791 815 1045 
%N A082131 Middle of semiprime triple. n-2, n, n+2 are semiprimes. 
%F A082131 a(1)=93 because 91=7*13, 93=3*31 and 95=5*19 are semiprime. 
%Y A082131 Cf. A001358, A082130 
%O A082131 1 
%K A082131 ,more,nonn, 
%A A082131 Hugo Pfoertner (hugo at pfoertner.org), Apr 04 2003

Is the semiprime cluster 213=3*71, 215=5*43,
217=7*31, 219=3*73, 221=13*17 the longest possible
run or can one find larger clusters?

Regards

Hugo





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