A242829 - OEIS

%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