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A259349 Numbers n such that n-1, n, and n+1 are all products of 6 distinct primes (i.e. belong to A067885).

%I A259349 #51 Jul 18 2023 09:50:25
%S A259349 1990586014,1994837494,2129658986,2341714794,2428906514,2963553594,
%T A259349 3297066410,3353808094,3373085990,3623442746,3659230730,3809238770,
%U A259349 3967387346,4058711734,4144727994,4196154390,4502893746,4555267690,4653623534
%N A259349 Numbers n such that n-1, n, and n+1 are all products of 6 distinct primes (i.e. belong to A067885).
%C A259349 A subsequence of A169834 and A067885.
%C A259349 The rudimentary method employed by the PARI program below reaches the limit of its usefulness here. Contrast it with the method required for A259350, which is over 4.5 orders of magnitude faster than the analog of this (and may still be some distance best).
%C A259349 a(1)=A093550(6) (that sequence's 5th term, with offset 2). The program arbitrarily makes use of this knowledge, but will run (slower) without it.
%H A259349 Giovanni Resta, <a href="/A259349/b259349.txt">Table of n, a(n) for n = 1..10000</a>
%F A259349 {n: A001221(n-1) = A001221(n) = A001221(n+1) = A001222(n-1) = A001222(n) = A001222(n+1) = 6}. - _R. J. Mathar_, Jul 18 2023
%e A259349 1990586013 = 3*13*29*67*109*241,
%e A259349 1990586014 = 2*23*37*43*59*461, and
%e A259349 1990586015 = 5*11*17*19*89*1259; and no smaller trio of this kind exists, making the middle value a(1).
%o A259349 (PARI)
%o A259349 {
%o A259349 \\Program initialized with known a(1).\\
%o A259349 \\The purpose of vector s and value u\\
%o A259349 \\is to skip bad values modulo 36.\\
%o A259349 k=1990586014;s=[4,4,8,8,8,4];u=1;
%o A259349 while(1,
%o A259349   if(issquarefree(k),
%o A259349     if(issquarefree(k-1),
%o A259349       if(issquarefree(k+1),
%o A259349         if(omega(k)==6,
%o A259349           if(omega(k-1)==6,
%o A259349             if(omega(k+1)==6,
%o A259349               print1(k" ")))))));
%o A259349   k+=s[u];if(u==6,u=1,u++))
%o A259349 }
%Y A259349 Cf. A093550, A169834, A364265, A248201, A248202, A248203, A248204, A259350, A259801.
%Y A259349 For products of 1, 2, 3, 4, 5, and 6 distinct primes see A000040, A006881, A007304, A046386, A046387, and A067885, resp.
%Y A259349 See A364265 for a closely related sequence. - _N. J. A. Sloane_, Jul 18 2023
%K A259349 nonn
%O A259349 1,1
%A A259349 _James G. Merickel_, Jun 24 2015