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%I #24 Jul 10 2015 20:02:54
%S 6639266409,8628052209,12692281897,14492398389,15798643881,
%T 18883291565,20404935965,20825703713,21342970293,21597222381,
%U 22221458853,22567169229,22578915665,23000623161,23198162685,23247729109,24163642653,24802386189,24894100941,26297281109
%N Integers n such that each of n, n+1, n+2, n+4, n+5, n+6 is the squarefree product of five primes.
%C This is a higher analog to A242804, A242805, A242806.
%C It is very tough to compute this sequence on a single machine. Therefore, the interval from 0 to 9*10^9 was subdivided into 9 partial intervals, of length 10^9 each, and scanned by different computers. Nevertheless the CPU time was extrapolated for a single machine and summed up to 30 hours for the first member 6639266409 and 47 hours (~2 days) for the second member 8628052209. Up to 10^10, there is no occurrence of a next term.
%H Jens Kruse Andersen, <a href="/A242829/b242829.txt">Table of n, a(n) for n = 1..195</a>
%e a(1) = 6639266409 = 3 * 29 * 109 * 421 * 1663,
%e 6639266410 = 2 * 5 * 7 * 113 * 839351,
%e 6639266411 = 17 * 23 * 89 * 101 * 1889,
%e 6639266413 = 13 * 61 * 79 * 131 * 809,
%e 6639266414 = 2 * 11 * 349 * 857 * 1009,
%e 6639266415 = 3 * 5 * 73 * 149 * 40693;
%e and
%e a(2) = 8628052209 = 3 * 7 * 19 * 863 * 25057,
%e 8628052210 = 2 * 5 * 251 * 953 * 3607,
%e 8628052211 = 17 * 43 * 179 * 233 * 283,
%e 8628052213 = 11 * 47 * 127 * 331 * 397,
%e 8628052214 = 2 * 53 * 107 * 131 * 5807,
%e 8628052215 = 3 * 5 * 23 * 31 * 806737.
%o (PARI)
%o { default(primelimit, 1000M); i=0; j=0; k=0; l=0; m=0; loc=0; lb=2; ub=9*10^9; o=5; for(n=lb, ub, if(issquarefree(n)&&(o==omega(n)), loc=loc+1; if(1==loc, i=n; ); if(2==loc, if(i+1==n, j=n; ); if(i+1<n, loc=1; i=n; ); ); if(3==loc, if(j+1==n, k=n; ); if(j+1<n, loc=1; i=n; ); ); if(4==loc, if(k+2==n, l=n; ); if(k+2<n, loc=1; i=n; ); ); if(5==loc, if(l+1==n, m=n; ); if(l+1<n, loc=1; i=n; ); ); if(6==loc, if(m+1==n, print1(i,","); loc=0; ); if(m+1<n, loc=1; i=n; ); ); ); ); }
%Y Cf. A242793 and A242804, A242805, A242806.
%K nonn
%O 1,1
%A _Daniel Constantin Mayer_, May 23 2014
%E More terms from _Jens Kruse Andersen_, Jun 18 2014
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