%I A113339
%S A113339 1,9,11,15,16,18,21,23,30,32,34,36,37,39,40,42,51,53,54,55,56,58,61,62,
%T A113339 66,67,68,71,73,74,76,80,82,84,86,96,100,101,102,103,105,106,107,108,
%U A113339 110,111,115,118,119,123,125,127,129,130,133,137,138,141,145,146,150
%N A113339 Integers n such that prime(n+1)-prime(n) is nonprime, square-free. Except 
               for the initial term of 1, the terms are k-semiprime for some k>=2.
%F A113339 prime(n+1)-prime(n)=1 or p1*...*pk where p1, ..., pk are two or more 
               distinct primes.
%e A113339 prime(69)-prime(68)=347-337=10=2*5.
%p A113339 L:=[]: for z to 1 do for k from 1 to 200 do p:=ithprime(k); q:=nextprime(p); 
               x:=q-p; if not(isprime(x)) and issqrfree(x) then L:=[op(L),k] fi 
               od od; L;
%Y A113339 Cf. A000040, A000469, A001358.
%Y A113339 Sequence in context: A027726 A044873 A101754 this_sequence A037009 A163096 
               A027694
%Y A113339 Adjacent sequences: A113336 A113337 A113338 this_sequence A113340 A113341 
               A113342
%K A113339 easy,nonn
%O A113339 1,2
%A A113339 Walter A. Kehowski (wkehowski(AT)cox.net), Jan 08 2006